TB01.ipynb

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    "# Juliaで学ぶタイトバインディング模型とトポロジカル物質\n",
    "## \n",
    "2022年3月21日 Julia 1.6以降で動作確認\n",
    "\n",
    "## 1. タイトバインディング模型とは何か？\n",
    "一次元シュレーディンガー方程式から始めて、タイトバインディング（強束縛）模型について理解することが目的である。  \n",
    "一次元シュレーディンガー方程式をなんとなく知っている程度で理解できるように書いたつもりである。  \n",
    "もし一次元シュレーディンガー方程式に馴染みがない場合には、\n",
    "「Juliaで学ぶ量子力学」  \n",
    "https://github.com/cometscome/QM   \n",
    "を参考にすると良いかもしれない。\n",
    "\n",
    "\n",
    "#### シュレーディンガー方程式から固体物理学へ\n",
    "一次元シュレーディンガー方程式から始めて、固体中での電子の挙動について調べてみよう。\n",
    "まず、固体中には原子が規則正しく並んでおり、原子は電子と原子核からなる。電子はマイナス、原子核はプラスの電荷を帯びているので、両者は引きつけあっている。電子から見ると、原子核の引き寄せの効果は引力ポテンシャルとして感じられる。量子力学の教科書で習うように、水素原子の場合には厳密に解くことができ、電子が水素原子核のまわりに束縛されていることがわかる。他の原子でも同様に、原子核は電子を束縛している。\n",
    "さて、ここで、原子を二つ並べて、だんだんと近づけていくと何が起こるだろうか？ 固体とは原子が規則正しく並んだものであり、原子同士が近くにあることが重要なはずである。原子二つの場合を見てから、一次元的に規則正しく並んだ場合を考えてみよう。もちろん、三次元的に並んでいるのが固体であるが、基本的な方針は変わらない。\n",
    "\n",
    "\n",
    "### 1.1 束縛状態を持つ1次元シュレーディンガー方程式\n",
    "#### 1.1.1 ポテンシャルを一つ持つ場合の束縛状態\n",
    "一次元系のシュレーディンガー方程式は、\n",
    "$$\n",
    "\\left( -\\frac{\\hbar^2}{2m}\\frac{d^2}{dx^2} + V(x) \\right) \\psi(x) = \\epsilon \\psi(x)\n",
    "$$\n",
    "である。無次元化しておくと、\n",
    "$$\n",
    "\\left( -\\frac{d^2}{dx^2} + V(x) \\right) \\psi(x) = \\epsilon \\psi(x)\n",
    "$$\n",
    "である。\n",
    "ここで、\n",
    "$$\n",
    "V(x) = V_0 \\exp(-x^2)\n",
    "$$"
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      "text/plain": [
       "V (generic function with 1 method)"
      ]
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   "source": [
    "V0 = -5.0\n",
    "V(x) =  V0*exp(-x^2)"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "というポテンシャルを考える。  \n",
    "形は"
   ]
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      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "N = 1000\n",
    "xmax = 10.0\n",
    "xmin = -10.0\n",
    "xvec = range(xmin,xmax,length=N)\n",
    "plot(xvec,V.(xvec),label=\"Potential\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "である。\n",
    "このポテンシャルを入れてシュレーディンガー方程式を解く。\n",
    "ここで、空間を差分化して、ハミルトニアンを行列："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "make_H1d (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function make_H1d(N,xmax,xmin,V)\n",
    "    mat_H = zeros(Float64,N,N)\n",
    "#    V(x) =  -V0*exp(-x^2/ξ^2)\n",
    "    a = (xmax-xmin)/(N-1)\n",
    "        \n",
    "    for i in 1:N\n",
    "        x = (i-1)*a + xmin\n",
    "        for dx in -1:1\n",
    "            j = i + dx\n",
    "            v = 0.0\n",
    "            if dx == 0                \n",
    "                v = (2/a^2 + V(x))\n",
    "            elseif dx == 1\n",
    "                v = -1/a^2\n",
    "            elseif dx == -1\n",
    "                v = -1/a^2\n",
    "            end\n",
    "            \n",
    "            if 1 <= j <= N\n",
    "                mat_H[i,j] = v\n",
    "            end\n",
    "            \n",
    "        end\n",
    "        \n",
    "    end\n",
    "    \n",
    "    return mat_H\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "とすることで、行列の対角化を行えばシュレーディンガー方程式を解くことができる。  \n",
    "実際に解いてエネルギー固有値を見てみると、"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.1404009040145286, -0.4062142205546486, 0.10339356506001751, 0.15632796480264988, 0.4145932097452478, 0.5822287366538306, 0.9363743175283377, 1.2355092013437883, 1.6711811288154879, 2.0989689480359477]\n"
     ]
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "mat_H = make_H1d(N,xmax,xmin,V) \n",
    "energy,mat_v = eigen(mat_H)\n",
    "println(energy[1:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "となる。最低エネルギー固有値の固有関数は"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "  619.858,1445.68 621.876,1445.68 623.893,1445.68 625.91,1445.68 627.928,1445.68 629.945,1445.68 631.963,1445.67 633.98,1445.67 635.997,1445.67 638.015,1445.67 \n",
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       "  720.729,1445.52 722.746,1445.51 724.764,1445.51 726.781,1445.5 728.798,1445.49 730.816,1445.48 732.833,1445.48 734.851,1445.47 736.868,1445.46 738.885,1445.45 \n",
       "  740.903,1445.44 742.92,1445.43 744.938,1445.42 746.955,1445.41 748.973,1445.4 750.99,1445.38 753.007,1445.37 755.025,1445.36 757.042,1445.35 759.06,1445.33 \n",
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       "  781.251,1445.15 783.269,1445.13 785.286,1445.11 787.303,1445.09 789.321,1445.07 791.338,1445.04 793.356,1445.02 795.373,1444.99 797.39,1444.97 799.408,1444.94 \n",
       "  801.425,1444.91 803.443,1444.88 805.46,1444.85 807.478,1444.82 809.495,1444.79 811.512,1444.76 813.53,1444.72 815.547,1444.69 817.565,1444.65 819.582,1444.61 \n",
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       "  841.774,1444.08 843.791,1444.02 845.808,1443.96 847.826,1443.9 849.843,1443.83 851.861,1443.77 853.878,1443.7 855.895,1443.62 857.913,1443.55 859.93,1443.47 \n",
       "  861.948,1443.39 863.965,1443.3 865.983,1443.22 868,1443.13 870.017,1443.03 872.035,1442.94 874.052,1442.84 876.07,1442.73 878.087,1442.62 880.104,1442.51 \n",
       "  882.122,1442.4 884.139,1442.28 886.157,1442.15 888.174,1442.02 890.192,1441.89 892.209,1441.75 894.226,1441.61 896.244,1441.46 898.261,1441.31 900.279,1441.15 \n",
       "  902.296,1440.98 904.313,1440.81 906.331,1440.64 908.348,1440.45 910.366,1440.26 912.383,1440.07 914.4,1439.86 916.418,1439.65 918.435,1439.43 920.453,1439.2 \n",
       "  922.47,1438.97 924.488,1438.73 926.505,1438.47 928.522,1438.21 930.54,1437.94 932.557,1437.66 934.575,1437.37 936.592,1437.07 938.609,1436.75 940.627,1436.43 \n",
       "  942.644,1436.1 944.662,1435.75 946.679,1435.39 948.697,1435.02 950.714,1434.63 952.731,1434.23 954.749,1433.81 956.766,1433.38 958.784,1432.94 960.801,1432.48 \n",
       "  962.818,1432 964.836,1431.5 966.853,1430.99 968.871,1430.46 970.888,1429.91 972.905,1429.34 974.923,1428.75 976.94,1428.13 978.958,1427.5 980.975,1426.84 \n",
       "  982.993,1426.16 985.01,1425.45 987.027,1424.72 989.045,1423.96 991.062,1423.18 993.08,1422.36 995.097,1421.52 997.114,1420.65 999.132,1419.74 1001.15,1418.8 \n",
       "  1003.17,1417.83 1005.18,1416.82 1007.2,1415.78 1009.22,1414.7 1011.24,1413.58 1013.25,1412.42 1015.27,1411.22 1017.29,1409.97 1019.31,1408.68 1021.32,1407.35 \n",
       "  1023.34,1405.96 1025.36,1404.53 1027.38,1403.04 1029.39,1401.5 1031.41,1399.9 1033.43,1398.25 1035.45,1396.54 1037.46,1394.76 1039.48,1392.92 1041.5,1391.02 \n",
       "  1043.51,1389.04 1045.53,1387 1047.55,1384.88 1049.57,1382.69 1051.58,1380.42 1053.6,1378.06 1055.62,1375.62 1057.64,1373.1 1059.65,1370.48 1061.67,1367.77 \n",
       "  1063.69,1364.96 1065.71,1362.06 1067.72,1359.05 1069.74,1355.93 1071.76,1352.7 1073.78,1349.35 1075.79,1345.89 1077.81,1342.3 1079.83,1338.59 1081.85,1334.74 \n",
       "  1083.86,1330.76 1085.88,1326.64 1087.9,1322.38 1089.92,1317.96 1091.93,1313.39 1093.95,1308.66 1095.97,1303.77 1097.99,1298.7 1100,1293.46 1102.02,1288.04 \n",
       "  1104.04,1282.43 1106.05,1276.63 1108.07,1270.63 1110.09,1264.43 1112.11,1258.02 1114.12,1251.39 1116.14,1244.54 1118.16,1237.46 1120.18,1230.14 1122.19,1222.58 \n",
       "  1124.21,1214.78 1126.23,1206.72 1128.25,1198.41 1130.26,1189.82 1132.28,1180.96 1134.3,1171.83 1136.32,1162.41 1138.33,1152.69 1140.35,1142.68 1142.37,1132.37 \n",
       "  1144.39,1121.75 1146.4,1110.81 1148.42,1099.55 1150.44,1087.97 1152.46,1076.06 1154.47,1063.82 1156.49,1051.25 1158.51,1038.33 1160.52,1025.07 1162.54,1011.47 \n",
       "  1164.56,997.518 1166.58,983.222 1168.59,968.58 1170.61,953.59 1172.63,938.256 1174.65,922.579 1176.66,906.562 1178.68,890.209 1180.7,873.526 1182.72,856.519 \n",
       "  1184.73,839.196 1186.75,821.564 1188.77,803.634 1190.79,785.416 1192.8,766.924 1194.82,748.17 1196.84,729.171 1198.86,709.942 1200.87,690.502 1202.89,670.871 \n",
       "  1204.91,651.069 1206.93,631.119 1208.94,611.044 1210.96,590.871 1212.98,570.627 1215,550.339 1217.01,530.038 1219.03,509.754 1221.05,489.521 1223.06,469.372 \n",
       "  1225.08,449.341 1227.1,429.465 1229.12,409.781 1231.13,390.326 1233.15,371.139 1235.17,352.258 1237.19,333.724 1239.2,315.576 1241.22,297.855 1243.24,280.6 \n",
       "  1245.26,263.852 1247.27,247.65 1249.29,232.033 1251.31,217.039 1253.33,202.707 1255.34,189.072 1257.36,176.171 1259.38,164.037 1261.4,152.702 1263.41,142.197 \n",
       "  1265.43,132.55 1267.45,123.789 1269.47,115.938 1271.48,109.018 1273.5,103.049 1275.52,98.0493 1277.53,94.0318 1279.55,91.0084 1281.57,88.988 1283.59,87.9763 \n",
       "  1285.6,87.9763 1287.62,88.988 1289.64,91.0084 1291.66,94.0318 1293.67,98.0493 1295.69,103.049 1297.71,109.018 1299.73,115.938 1301.74,123.789 1303.76,132.55 \n",
       "  1305.78,142.197 1307.8,152.702 1309.81,164.037 1311.83,176.171 1313.85,189.072 1315.87,202.707 1317.88,217.039 1319.9,232.033 1321.92,247.65 1323.94,263.852 \n",
       "  1325.95,280.6 1327.97,297.855 1329.99,315.576 1332.01,333.724 1334.02,352.258 1336.04,371.139 1338.06,390.326 1340.07,409.781 1342.09,429.465 1344.11,449.341 \n",
       "  1346.13,469.372 1348.14,489.521 1350.16,509.754 1352.18,530.038 1354.2,550.339 1356.21,570.627 1358.23,590.871 1360.25,611.044 1362.27,631.119 1364.28,651.069 \n",
       "  1366.3,670.871 1368.32,690.502 1370.34,709.942 1372.35,729.171 1374.37,748.17 1376.39,766.924 1378.41,785.416 1380.42,803.634 1382.44,821.564 1384.46,839.196 \n",
       "  1386.48,856.519 1388.49,873.526 1390.51,890.209 1392.53,906.562 1394.54,922.579 1396.56,938.256 1398.58,953.59 1400.6,968.58 1402.61,983.222 1404.63,997.518 \n",
       "  1406.65,1011.47 1408.67,1025.07 1410.68,1038.33 1412.7,1051.25 1414.72,1063.82 1416.74,1076.06 1418.75,1087.97 1420.77,1099.55 1422.79,1110.81 1424.81,1121.75 \n",
       "  1426.82,1132.37 1428.84,1142.68 1430.86,1152.69 1432.88,1162.41 1434.89,1171.83 1436.91,1180.96 1438.93,1189.82 1440.95,1198.41 1442.96,1206.72 1444.98,1214.78 \n",
       "  1447,1222.58 1449.02,1230.14 1451.03,1237.46 1453.05,1244.54 1455.07,1251.39 1457.08,1258.02 1459.1,1264.43 1461.12,1270.63 1463.14,1276.63 1465.15,1282.43 \n",
       "  1467.17,1288.04 1469.19,1293.46 1471.21,1298.7 1473.22,1303.77 1475.24,1308.66 1477.26,1313.39 1479.28,1317.96 1481.29,1322.38 1483.31,1326.64 1485.33,1330.76 \n",
       "  1487.35,1334.74 1489.36,1338.59 1491.38,1342.3 1493.4,1345.89 1495.42,1349.35 1497.43,1352.7 1499.45,1355.93 1501.47,1359.05 1503.49,1362.06 1505.5,1364.96 \n",
       "  1507.52,1367.77 1509.54,1370.48 1511.55,1373.1 1513.57,1375.62 1515.59,1378.06 1517.61,1380.42 1519.62,1382.69 1521.64,1384.88 1523.66,1387 1525.68,1389.04 \n",
       "  1527.69,1391.02 1529.71,1392.92 1531.73,1394.76 1533.75,1396.54 1535.76,1398.25 1537.78,1399.9 1539.8,1401.5 1541.82,1403.04 1543.83,1404.53 1545.85,1405.96 \n",
       "  1547.87,1407.35 1549.89,1408.68 1551.9,1409.97 1553.92,1411.22 1555.94,1412.42 1557.96,1413.58 1559.97,1414.7 1561.99,1415.78 1564.01,1416.82 1566.03,1417.83 \n",
       "  1568.04,1418.8 1570.06,1419.74 1572.08,1420.65 1574.09,1421.52 1576.11,1422.36 1578.13,1423.18 1580.15,1423.96 1582.16,1424.72 1584.18,1425.45 1586.2,1426.16 \n",
       "  1588.22,1426.84 1590.23,1427.5 1592.25,1428.13 1594.27,1428.75 1596.29,1429.34 1598.3,1429.91 1600.32,1430.46 1602.34,1430.99 1604.36,1431.5 1606.37,1432 \n",
       "  1608.39,1432.48 1610.41,1432.94 1612.43,1433.38 1614.44,1433.81 1616.46,1434.23 1618.48,1434.63 1620.5,1435.02 1622.51,1435.39 1624.53,1435.75 1626.55,1436.1 \n",
       "  1628.56,1436.43 1630.58,1436.75 1632.6,1437.07 1634.62,1437.37 1636.63,1437.66 1638.65,1437.94 1640.67,1438.21 1642.69,1438.47 1644.7,1438.73 1646.72,1438.97 \n",
       "  1648.74,1439.2 1650.76,1439.43 1652.77,1439.65 1654.79,1439.86 1656.81,1440.07 1658.83,1440.26 1660.84,1440.45 1662.86,1440.64 1664.88,1440.81 1666.9,1440.98 \n",
       "  1668.91,1441.15 1670.93,1441.31 1672.95,1441.46 1674.97,1441.61 1676.98,1441.75 1679,1441.89 1681.02,1442.02 1683.04,1442.15 1685.05,1442.28 1687.07,1442.4 \n",
       "  1689.09,1442.51 1691.1,1442.62 1693.12,1442.73 1695.14,1442.84 1697.16,1442.94 1699.17,1443.03 1701.19,1443.13 1703.21,1443.22 1705.23,1443.3 1707.24,1443.39 \n",
       "  1709.26,1443.47 1711.28,1443.55 1713.3,1443.62 1715.31,1443.7 1717.33,1443.77 1719.35,1443.83 1721.37,1443.9 1723.38,1443.96 1725.4,1444.02 1727.42,1444.08 \n",
       "  1729.44,1444.14 1731.45,1444.2 1733.47,1444.25 1735.49,1444.3 1737.51,1444.35 1739.52,1444.4 1741.54,1444.44 1743.56,1444.49 1745.57,1444.53 1747.59,1444.57 \n",
       "  1749.61,1444.61 1751.63,1444.65 1753.64,1444.69 1755.66,1444.72 1757.68,1444.76 1759.7,1444.79 1761.71,1444.82 1763.73,1444.85 1765.75,1444.88 1767.77,1444.91 \n",
       "  1769.78,1444.94 1771.8,1444.97 1773.82,1444.99 1775.84,1445.02 1777.85,1445.04 1779.87,1445.07 1781.89,1445.09 1783.91,1445.11 1785.92,1445.13 1787.94,1445.15 \n",
       "  1789.96,1445.17 1791.98,1445.19 1793.99,1445.21 1796.01,1445.23 1798.03,1445.24 1800.05,1445.26 1802.06,1445.28 1804.08,1445.29 1806.1,1445.31 1808.11,1445.32 \n",
       "  1810.13,1445.33 1812.15,1445.35 1814.17,1445.36 1816.18,1445.37 1818.2,1445.38 1820.22,1445.4 1822.24,1445.41 1824.25,1445.42 1826.27,1445.43 1828.29,1445.44 \n",
       "  1830.31,1445.45 1832.32,1445.46 1834.34,1445.47 1836.36,1445.48 1838.38,1445.48 1840.39,1445.49 1842.41,1445.5 1844.43,1445.51 1846.45,1445.51 1848.46,1445.52 \n",
       "  1850.48,1445.53 1852.5,1445.53 1854.52,1445.54 1856.53,1445.55 1858.55,1445.55 1860.57,1445.56 1862.58,1445.56 1864.6,1445.57 1866.62,1445.57 1868.64,1445.58 \n",
       "  1870.65,1445.58 1872.67,1445.59 1874.69,1445.59 1876.71,1445.6 1878.72,1445.6 1880.74,1445.61 1882.76,1445.61 1884.78,1445.61 1886.79,1445.62 1888.81,1445.62 \n",
       "  1890.83,1445.62 1892.85,1445.63 1894.86,1445.63 1896.88,1445.63 1898.9,1445.64 1900.92,1445.64 1902.93,1445.64 1904.95,1445.64 1906.97,1445.65 1908.99,1445.65 \n",
       "  1911,1445.65 1913.02,1445.65 1915.04,1445.66 1917.06,1445.66 1919.07,1445.66 1921.09,1445.66 1923.11,1445.66 1925.12,1445.67 1927.14,1445.67 1929.16,1445.67 \n",
       "  1931.18,1445.67 1933.19,1445.67 1935.21,1445.67 1937.23,1445.67 1939.25,1445.68 1941.26,1445.68 1943.28,1445.68 1945.3,1445.68 1947.32,1445.68 1949.33,1445.68 \n",
       "  1951.35,1445.68 1953.37,1445.68 1955.39,1445.69 1957.4,1445.69 1959.42,1445.69 1961.44,1445.69 1963.46,1445.69 1965.47,1445.69 1967.49,1445.69 1969.51,1445.69 \n",
       "  1971.53,1445.69 1973.54,1445.69 1975.56,1445.69 1977.58,1445.7 1979.59,1445.7 1981.61,1445.7 1983.63,1445.7 1985.65,1445.7 1987.66,1445.7 1989.68,1445.7 \n",
       "  1991.7,1445.7 1993.72,1445.7 1995.73,1445.7 1997.75,1445.7 1999.77,1445.7 2001.79,1445.7 2003.8,1445.7 2005.82,1445.7 2007.84,1445.7 2009.86,1445.7 \n",
       "  2011.87,1445.7 2013.89,1445.71 2015.91,1445.71 2017.93,1445.71 2019.94,1445.71 2021.96,1445.71 2023.98,1445.71 2026,1445.71 2028.01,1445.71 2030.03,1445.71 \n",
       "  2032.05,1445.71 2034.07,1445.71 2036.08,1445.71 2038.1,1445.71 2040.12,1445.71 2042.13,1445.71 2044.15,1445.71 2046.17,1445.71 2048.19,1445.71 2050.2,1445.71 \n",
       "  2052.22,1445.71 2054.24,1445.71 2056.26,1445.71 2058.27,1445.71 2060.29,1445.71 2062.31,1445.71 2064.33,1445.71 2066.34,1445.71 2068.36,1445.71 2070.38,1445.71 \n",
       "  2072.4,1445.71 2074.41,1445.71 2076.43,1445.71 2078.45,1445.71 2080.47,1445.71 2082.48,1445.71 2084.5,1445.71 2086.52,1445.71 2088.54,1445.71 2090.55,1445.71 \n",
       "  2092.57,1445.71 2094.59,1445.71 2096.6,1445.71 2098.62,1445.71 2100.64,1445.71 2102.66,1445.71 2104.67,1445.71 2106.69,1445.71 2108.71,1445.71 2110.73,1445.71 \n",
       "  2112.74,1445.71 2114.76,1445.71 2116.78,1445.71 2118.8,1445.71 2120.81,1445.71 2122.83,1445.71 2124.85,1445.71 2126.87,1445.71 2128.88,1445.71 2130.9,1445.71 \n",
       "  2132.92,1445.71 2134.94,1445.71 2136.95,1445.71 2138.97,1445.71 2140.99,1445.71 2143.01,1445.71 2145.02,1445.71 2147.04,1445.71 2149.06,1445.71 2151.08,1445.71 \n",
       "  2153.09,1445.71 2155.11,1445.71 2157.13,1445.71 2159.14,1445.71 2161.16,1445.71 2163.18,1445.71 2165.2,1445.71 2167.21,1445.71 2169.23,1445.72 2171.25,1445.72 \n",
       "  2173.27,1445.72 2175.28,1445.72 2177.3,1445.72 2179.32,1445.72 2181.34,1445.72 2183.35,1445.72 2185.37,1445.72 2187.39,1445.72 2189.41,1445.72 2191.42,1445.72 \n",
       "  2193.44,1445.72 2195.46,1445.72 2197.48,1445.72 2199.49,1445.72 2201.51,1445.72 2203.53,1445.72 2205.55,1445.72 2207.56,1445.72 2209.58,1445.72 2211.6,1445.72 \n",
       "  2213.61,1445.72 2215.63,1445.72 2217.65,1445.72 2219.67,1445.72 2221.68,1445.72 2223.7,1445.72 2225.72,1445.72 2227.74,1445.72 2229.75,1445.72 2231.77,1445.72 \n",
       "  2233.79,1445.72 2235.81,1445.72 2237.82,1445.72 2239.84,1445.72 2241.86,1445.72 2243.88,1445.72 2245.89,1445.72 2247.91,1445.72 2249.93,1445.72 2251.95,1445.72 \n",
       "  2253.96,1445.72 2255.98,1445.72 2258,1445.72 2260.02,1445.72 2262.03,1445.72 2264.05,1445.72 2266.07,1445.72 2268.09,1445.72 2270.1,1445.72 2272.12,1445.72 \n",
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      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "plot(xvec,[mat_v[:,1]],label=\"Wavefunction\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "となり、ポテンシャルに束縛されている。  \n",
    "#### 1.1.2 ポテンシャルを二つ持つ場合の束縛状態:遠い場合\n",
    "次に、このポテンシャルを二つ並べてみよう。$x = \\pm x_0$の二点にガウス関数を設定する。\n",
    "$$\n",
    "V(x) = V_0 (\\exp(-(x-x0)^2) + \\exp(-(x+x_0)^2))\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "  544.502,141.768 546.583,145.758 548.664,149.993 550.745,154.486 552.826,159.247 554.907,164.288 556.988,169.619 559.069,175.254 561.15,181.202 563.231,187.476 \n",
       "  565.312,194.087 567.393,201.046 569.473,208.366 571.554,216.057 573.635,224.129 575.716,232.595 577.797,241.464 579.878,250.746 581.959,260.451 584.04,270.589 \n",
       "  586.121,281.167 588.202,292.195 590.283,303.679 592.364,315.626 594.444,328.042 596.525,340.933 598.606,354.302 600.687,368.153 602.768,382.489 604.849,397.31 \n",
       "  606.93,412.616 609.011,428.407 611.092,444.68 613.173,461.431 615.254,478.655 617.335,496.347 619.415,514.497 621.496,533.098 623.577,552.137 625.658,571.603 \n",
       "  627.739,591.481 629.82,611.757 631.901,632.412 633.982,653.428 636.063,674.785 638.144,696.461 640.225,718.432 642.305,740.673 644.386,763.157 646.467,785.855 \n",
       "  648.548,808.739 650.629,831.777 652.71,854.936 654.791,878.183 656.872,901.482 658.953,924.796 661.034,948.089 663.115,971.322 665.196,994.456 667.276,1017.45 \n",
       "  669.357,1040.26 671.438,1062.86 673.519,1085.18 675.6,1107.21 677.681,1128.88 679.762,1150.16 681.843,1171.01 683.924,1191.39 686.005,1211.24 688.086,1230.54 \n",
       "  690.167,1249.24 692.247,1267.3 694.328,1284.68 696.409,1301.34 698.49,1317.25 700.571,1332.37 702.652,1346.66 704.733,1360.1 706.814,1372.66 708.895,1384.3 \n",
       "  710.976,1394.99 713.057,1404.72 715.138,1413.45 717.218,1421.18 719.299,1427.88 721.38,1433.53 723.461,1438.12 725.542,1441.64 727.623,1444.08 729.704,1445.44 \n",
       "  731.785,1445.72 733.866,1444.9 735.947,1443 738.028,1440.01 740.109,1435.96 742.189,1430.83 744.27,1424.66 746.351,1417.44 748.432,1409.21 750.513,1399.98 \n",
       "  752.594,1389.76 754.675,1378.59 756.756,1366.49 758.837,1353.49 760.918,1339.62 762.999,1324.91 765.08,1309.39 767.16,1293.1 769.241,1276.08 771.322,1258.35 \n",
       "  773.403,1239.97 775.484,1220.97 777.565,1201.38 779.646,1181.26 781.727,1160.65 783.808,1139.57 785.889,1118.09 787.97,1096.24 790.051,1074.06 792.131,1051.59 \n",
       "  794.212,1028.88 796.293,1005.97 798.374,982.904 800.455,959.716 802.536,936.448 804.617,913.139 806.698,889.828 808.779,866.551 810.86,843.344 812.941,820.241 \n",
       "  815.022,797.276 817.102,774.481 819.183,751.886 821.264,729.52 823.345,707.411 825.426,685.585 827.507,664.066 829.588,642.876 831.669,622.038 833.75,601.57 \n",
       "  835.831,581.491 837.912,561.817 839.993,542.563 842.073,523.742 844.154,505.365 846.235,487.443 848.316,469.984 850.397,452.996 852.478,436.483 854.559,420.451 \n",
       "  856.64,404.902 858.721,389.838 860.802,375.26 862.883,361.167 864.963,347.557 867.044,334.428 869.125,321.775 871.206,309.594 873.287,297.879 875.368,286.624 \n",
       "  877.449,275.822 879.53,265.465 881.611,255.545 883.692,246.053 885.773,236.978 887.854,228.312 889.934,220.044 892.015,212.164 894.096,204.66 896.177,197.522 \n",
       "  898.258,190.738 900.339,184.297 902.42,178.188 904.501,172.398 906.582,166.916 908.663,161.732 910.744,156.832 912.825,152.207 914.905,147.844 916.986,143.733 \n",
       "  919.067,139.862 921.148,136.222 923.229,132.801 925.31,129.589 927.391,126.577 929.472,123.753 931.553,121.11 933.634,118.638 935.715,116.327 937.796,114.169 \n",
       "  939.876,112.156 941.957,110.28 944.038,108.533 946.119,106.908 948.2,105.397 950.281,103.994 952.362,102.692 954.443,101.485 956.524,100.367 958.605,99.333 \n",
       "  960.686,98.3766 962.767,97.4931 964.847,96.6777 966.928,95.9257 969.009,95.2329 971.09,94.5952 973.171,94.0087 975.252,93.4698 977.333,92.975 979.414,92.5211 \n",
       "  981.495,92.1051 983.576,91.7242 985.657,91.3757 987.738,91.0571 989.818,90.7662 991.899,90.5007 993.98,90.2586 996.061,90.0381 998.142,89.8374 1000.22,89.6549 \n",
       "  1002.3,89.4891 1004.38,89.3386 1006.47,89.202 1008.55,89.0783 1010.63,88.9663 1012.71,88.8649 1014.79,88.7733 1016.87,88.6905 1018.95,88.6159 1021.03,88.5485 \n",
       "  1023.11,88.4879 1025.19,88.4333 1027.27,88.3842 1029.36,88.3401 1031.44,88.3005 1033.52,88.265 1035.6,88.2332 1037.68,88.2046 1039.76,88.1791 1041.84,88.1563 \n",
       "  1043.92,88.136 1046,88.1178 1048.08,88.1016 1050.17,88.0871 1052.25,88.0743 1054.33,88.0629 1056.41,88.0527 1058.49,88.0437 1060.57,88.0357 1062.65,88.0286 \n",
       "  1064.73,88.0223 1066.81,88.0167 1068.89,88.0118 1070.97,88.0075 1073.06,88.0036 1075.14,88.0002 1077.22,87.9973 1079.3,87.9946 1081.38,87.9923 1083.46,87.9903 \n",
       "  1085.54,87.9885 1087.62,87.9869 1089.7,87.9856 1091.78,87.9844 1093.86,87.9833 1095.95,87.9824 1098.03,87.9816 1100.11,87.9809 1102.19,87.9803 1104.27,87.9797 \n",
       "  1106.35,87.9793 1108.43,87.9789 1110.51,87.9785 1112.59,87.9782 1114.67,87.978 1116.75,87.9777 1118.84,87.9775 1120.92,87.9773 1123,87.9772 1125.08,87.9771 \n",
       "  1127.16,87.977 1129.24,87.9769 1131.32,87.9768 1133.4,87.9767 1135.48,87.9766 1137.56,87.9766 1139.64,87.9765 1141.73,87.9765 1143.81,87.9765 1145.89,87.9764 \n",
       "  1147.97,87.9764 1150.05,87.9764 1152.13,87.9764 1154.21,87.9764 1156.29,87.9764 1158.37,87.9763 1160.45,87.9763 1162.53,87.9763 1164.62,87.9763 1166.7,87.9763 \n",
       "  1168.78,87.9763 1170.86,87.9763 1172.94,87.9763 1175.02,87.9763 1177.1,87.9763 1179.18,87.9763 1181.26,87.9763 1183.34,87.9763 1185.42,87.9763 1187.51,87.9763 \n",
       "  1189.59,87.9763 1191.67,87.9763 1193.75,87.9763 1195.83,87.9763 1197.91,87.9763 1199.99,87.9763 1202.07,87.9763 1204.15,87.9763 1206.23,87.9763 1208.31,87.9763 \n",
       "  1210.4,87.9763 1212.48,87.9763 1214.56,87.9763 1216.64,87.9763 1218.72,87.9763 1220.8,87.9763 1222.88,87.9763 1224.96,87.9763 1227.04,87.9763 1229.12,87.9763 \n",
       "  1231.2,87.9763 1233.29,87.9763 1235.37,87.9763 1237.45,87.9763 1239.53,87.9763 1241.61,87.9763 1243.69,87.9763 1245.77,87.9763 1247.85,87.9763 1249.93,87.9763 \n",
       "  1252.01,87.9763 1254.09,87.9763 1256.18,87.9763 1258.26,87.9763 1260.34,87.9763 1262.42,87.9763 1264.5,87.9763 1266.58,87.9763 1268.66,87.9763 1270.74,87.9763 \n",
       "  1272.82,87.9763 1274.9,87.9763 1276.98,87.9763 1279.07,87.9763 1281.15,87.9763 1283.23,87.9763 1285.31,87.9763 1287.39,87.9763 1289.47,87.9763 1291.55,87.9763 \n",
       "  1293.63,87.9763 1295.71,87.9763 1297.79,87.9763 1299.87,87.9763 1301.96,87.9763 1304.04,87.9763 1306.12,87.9763 1308.2,87.9763 1310.28,87.9763 1312.36,87.9763 \n",
       "  1314.44,87.9763 1316.52,87.9763 1318.6,87.9763 1320.68,87.9763 1322.76,87.9763 1324.85,87.9763 1326.93,87.9763 1329.01,87.9763 1331.09,87.9763 1333.17,87.9763 \n",
       "  1335.25,87.9763 1337.33,87.9763 1339.41,87.9763 1341.49,87.9763 1343.57,87.9763 1345.66,87.9764 1347.74,87.9764 1349.82,87.9764 1351.9,87.9764 1353.98,87.9764 \n",
       "  1356.06,87.9764 1358.14,87.9765 1360.22,87.9765 1362.3,87.9765 1364.38,87.9766 1366.46,87.9766 1368.55,87.9767 1370.63,87.9768 1372.71,87.9769 1374.79,87.977 \n",
       "  1376.87,87.9771 1378.95,87.9772 1381.03,87.9773 1383.11,87.9775 1385.19,87.9777 1387.27,87.978 1389.35,87.9782 1391.44,87.9785 1393.52,87.9789 1395.6,87.9793 \n",
       "  1397.68,87.9797 1399.76,87.9803 1401.84,87.9809 1403.92,87.9816 1406,87.9824 1408.08,87.9833 1410.16,87.9844 1412.24,87.9856 1414.33,87.9869 1416.41,87.9885 \n",
       "  1418.49,87.9903 1420.57,87.9923 1422.65,87.9946 1424.73,87.9973 1426.81,88.0002 1428.89,88.0036 1430.97,88.0075 1433.05,88.0118 1435.13,88.0167 1437.22,88.0223 \n",
       "  1439.3,88.0286 1441.38,88.0357 1443.46,88.0437 1445.54,88.0527 1447.62,88.0629 1449.7,88.0743 1451.78,88.0871 1453.86,88.1016 1455.94,88.1178 1458.02,88.136 \n",
       "  1460.11,88.1563 1462.19,88.1791 1464.27,88.2046 1466.35,88.2332 1468.43,88.265 1470.51,88.3005 1472.59,88.3401 1474.67,88.3842 1476.75,88.4333 1478.83,88.4879 \n",
       "  1480.91,88.5485 1483,88.6159 1485.08,88.6905 1487.16,88.7733 1489.24,88.8649 1491.32,88.9663 1493.4,89.0783 1495.48,89.202 1497.56,89.3386 1499.64,89.4891 \n",
       "  1501.72,89.6549 1503.8,89.8374 1505.89,90.0381 1507.97,90.2586 1510.05,90.5007 1512.13,90.7662 1514.21,91.0571 1516.29,91.3757 1518.37,91.7242 1520.45,92.1051 \n",
       "  1522.53,92.5211 1524.61,92.975 1526.69,93.4698 1528.78,94.0087 1530.86,94.5952 1532.94,95.2329 1535.02,95.9257 1537.1,96.6777 1539.18,97.4931 1541.26,98.3766 \n",
       "  1543.34,99.333 1545.42,100.367 1547.5,101.485 1549.58,102.692 1551.67,103.994 1553.75,105.397 1555.83,106.908 1557.91,108.533 1559.99,110.28 1562.07,112.156 \n",
       "  1564.15,114.169 1566.23,116.327 1568.31,118.638 1570.39,121.11 1572.47,123.753 1574.56,126.577 1576.64,129.589 1578.72,132.801 1580.8,136.222 1582.88,139.862 \n",
       "  1584.96,143.733 1587.04,147.844 1589.12,152.207 1591.2,156.832 1593.28,161.732 1595.36,166.916 1597.45,172.398 1599.53,178.188 1601.61,184.297 1603.69,190.738 \n",
       "  1605.77,197.522 1607.85,204.66 1609.93,212.164 1612.01,220.044 1614.09,228.312 1616.17,236.978 1618.26,246.053 1620.34,255.545 1622.42,265.465 1624.5,275.822 \n",
       "  1626.58,286.624 1628.66,297.879 1630.74,309.594 1632.82,321.775 1634.9,334.428 1636.98,347.557 1639.06,361.167 1641.15,375.26 1643.23,389.838 1645.31,404.902 \n",
       "  1647.39,420.451 1649.47,436.483 1651.55,452.996 1653.63,469.984 1655.71,487.443 1657.79,505.365 1659.87,523.742 1661.95,542.563 1664.04,561.817 1666.12,581.491 \n",
       "  1668.2,601.57 1670.28,622.038 1672.36,642.876 1674.44,664.066 1676.52,685.585 1678.6,707.411 1680.68,729.52 1682.76,751.886 1684.84,774.481 1686.93,797.276 \n",
       "  1689.01,820.241 1691.09,843.344 1693.17,866.551 1695.25,889.828 1697.33,913.139 1699.41,936.448 1701.49,959.716 1703.57,982.904 1705.65,1005.97 1707.73,1028.88 \n",
       "  1709.82,1051.59 1711.9,1074.06 1713.98,1096.24 1716.06,1118.09 1718.14,1139.57 1720.22,1160.65 1722.3,1181.26 1724.38,1201.38 1726.46,1220.97 1728.54,1239.97 \n",
       "  1730.62,1258.35 1732.71,1276.08 1734.79,1293.1 1736.87,1309.39 1738.95,1324.91 1741.03,1339.62 1743.11,1353.49 1745.19,1366.49 1747.27,1378.59 1749.35,1389.76 \n",
       "  1751.43,1399.98 1753.51,1409.21 1755.6,1417.44 1757.68,1424.66 1759.76,1430.83 1761.84,1435.96 1763.92,1440.01 1766,1443 1768.08,1444.9 1770.16,1445.72 \n",
       "  1772.24,1445.44 1774.32,1444.08 1776.4,1441.64 1778.49,1438.12 1780.57,1433.53 1782.65,1427.88 1784.73,1421.18 1786.81,1413.45 1788.89,1404.72 1790.97,1394.99 \n",
       "  1793.05,1384.3 1795.13,1372.66 1797.21,1360.1 1799.29,1346.66 1801.38,1332.37 1803.46,1317.25 1805.54,1301.34 1807.62,1284.68 1809.7,1267.3 1811.78,1249.24 \n",
       "  1813.86,1230.54 1815.94,1211.24 1818.02,1191.39 1820.1,1171.01 1822.18,1150.16 1824.27,1128.88 1826.35,1107.21 1828.43,1085.18 1830.51,1062.86 1832.59,1040.26 \n",
       "  1834.67,1017.45 1836.75,994.456 1838.83,971.322 1840.91,948.089 1842.99,924.796 1845.07,901.482 1847.16,878.183 1849.24,854.936 1851.32,831.777 1853.4,808.739 \n",
       "  1855.48,785.855 1857.56,763.157 1859.64,740.673 1861.72,718.432 1863.8,696.461 1865.88,674.785 1867.96,653.428 1870.05,632.412 1872.13,611.757 1874.21,591.481 \n",
       "  1876.29,571.603 1878.37,552.137 1880.45,533.098 1882.53,514.497 1884.61,496.347 1886.69,478.655 1888.77,461.431 1890.86,444.68 1892.94,428.407 1895.02,412.616 \n",
       "  1897.1,397.31 1899.18,382.489 1901.26,368.153 1903.34,354.302 1905.42,340.933 1907.5,328.042 1909.58,315.626 1911.66,303.679 1913.75,292.195 1915.83,281.167 \n",
       "  1917.91,270.589 1919.99,260.451 1922.07,250.746 1924.15,241.464 1926.23,232.595 1928.31,224.129 1930.39,216.057 1932.47,208.366 1934.55,201.046 1936.64,194.087 \n",
       "  1938.72,187.476 1940.8,181.202 1942.88,175.254 1944.96,169.619 1947.04,164.288 1949.12,159.247 1951.2,154.486 1953.28,149.993 1955.36,145.758 1957.44,141.768 \n",
       "  1959.53,138.014 1961.61,134.485 1963.69,131.17 1965.77,128.059 1967.85,125.142 1969.93,122.41 1972.01,119.853 1974.09,117.462 1976.17,115.229 1978.25,113.145 \n",
       "  1980.33,111.202 1982.42,109.391 1984.5,107.706 1986.58,106.139 1988.66,104.683 1990.74,103.331 1992.82,102.077 1994.9,100.916 1996.98,99.8402 1999.06,98.8454 \n",
       "  2001.14,97.926 2003.22,97.0772 2005.31,96.294 2007.39,95.5722 2009.47,94.9074 2011.55,94.2958 2013.63,93.7335 2015.71,93.217 2017.79,92.7431 2019.87,92.3085 \n",
       "  2021.95,91.9104 2024.03,91.546 2026.11,91.2128 2028.2,90.9083 2030.28,90.6304 2032.36,90.3768 2034.44,90.1458 2036.52,89.9354 2038.6,89.744 2040.68,89.57 \n",
       "  2042.76,89.412 2044.84,89.2686 2046.92,89.1386 2049,89.0209 2051.09,88.9143 2053.17,88.8179 2055.25,88.7308 2057.33,88.6522 2059.41,88.5813 2061.49,88.5174 \n",
       "  2063.57,88.4599 2065.65,88.4081 2067.73,88.3616 2069.81,88.3198 2071.89,88.2823 2073.98,88.2486 2076.06,88.2185 2078.14,88.1915 2080.22,88.1674 2082.3,88.1459 \n",
       "  2084.38,88.1266 2086.46,88.1095 2088.54,88.0942 2090.62,88.0805 2092.7,88.0684 2094.78,88.0576 2096.87,88.048 2098.95,88.0395 2101.03,88.032 2103.11,88.0253 \n",
       "  2105.19,88.0194 2107.27,88.0142 2109.35,88.0096 2111.43,88.0055 2113.51,88.0019 2115.59,87.9987 2117.67,87.9959 2119.76,87.9934 2121.84,87.9913 2123.92,87.9894 \n",
       "  2126,87.9877 2128.08,87.9862 2130.16,87.985 2132.24,87.9838 2134.32,87.9828 2136.4,87.982 2138.48,87.9812 2140.56,87.9806 2142.65,87.98 2144.73,87.9795 \n",
       "  2146.81,87.9791 2148.89,87.9787 2150.97,87.9784 2153.05,87.9781 2155.13,87.9778 2157.21,87.9776 2159.29,87.9774 2161.37,87.9773 2163.45,87.9771 2165.54,87.977 \n",
       "  2167.62,87.9769 2169.7,87.9768 2171.78,87.9767 2173.86,87.9767 2175.94,87.9766 2178.02,87.9766 2180.1,87.9765 2182.18,87.9765 2184.26,87.9765 2186.35,87.9764 \n",
       "  2188.43,87.9764 2190.51,87.9764 2192.59,87.9764 2194.67,87.9764 2196.75,87.9763 2198.83,87.9763 2200.91,87.9763 2202.99,87.9763 2205.07,87.9763 2207.15,87.9763 \n",
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      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = 5\n",
    "V2(x) =  V0*(exp(-(x-x0)^2)+exp(-(x+x0)^2))\n",
    "plot(xvec,V2.(xvec),label=\"Potential\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$x_0$が大きければポテンシャル同士は離れているため、それぞれを別々に解いた場合と固有値は変わらない。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ポテンシャル二つの時のエネルギー\n",
      "[-3.140400933741141, -3.140400065868767, -0.40629704558980606, -0.39915370914881443, 0.16695946318332, 0.43793595314145595, 0.6183564602667886, 0.8782890894556825, 1.318612572162074, 1.780767230755412]\n",
      "ポテンシャル一つの時のエネルギー\n",
      "[-3.1404009040145286, -0.4062142205546486, 0.10339356506001751, 0.15632796480264988, 0.4145932097452478, 0.5822287366538306, 0.9363743175283377, 1.2355092013437883, 1.6711811288154879, 2.0989689480359477]\n"
     ]
    }
   ],
   "source": [
    "mat_H2 = make_H1d(N,xmax,xmin,V2) \n",
    "energy2p,mat_v2 = eigen(mat_H2)\n",
    "println(\"ポテンシャル二つの時のエネルギー\")\n",
    "println(energy2p[1:10])\n",
    "println(\"ポテンシャル一つの時のエネルギー\")\n",
    "println(energy[1:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "二つのポテンシャルに対応して二つの同じエネルギーの束縛状態がある。この二つは縮退しているので、固有関数は別々に解いた解の線形結合となる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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       "  373.102,766.126 375.084,766.094 377.065,766.061 379.047,766.026 381.029,765.991 383.01,765.955 384.992,765.917 386.974,765.879 388.956,765.839 390.937,765.798 \n",
       "  392.919,765.755 394.901,765.711 396.882,765.666 398.864,765.619 400.846,765.571 402.827,765.521 404.809,765.469 406.791,765.416 408.773,765.361 410.754,765.304 \n",
       "  412.736,765.245 414.718,765.184 416.699,765.121 418.681,765.056 420.663,764.989 422.644,764.919 424.626,764.847 426.608,764.772 428.589,764.695 430.571,764.615 \n",
       "  432.553,764.532 434.535,764.446 436.516,764.357 438.498,764.265 440.48,764.17 442.461,764.072 444.443,763.97 446.425,763.864 448.406,763.755 450.388,763.641 \n",
       "  452.37,763.524 454.351,763.402 456.333,763.277 458.315,763.146 460.297,763.011 462.278,762.872 464.26,762.727 466.242,762.577 468.223,762.421 470.205,762.26 \n",
       "  472.187,762.094 474.168,761.921 476.15,761.742 478.132,761.557 480.114,761.365 482.095,761.166 484.077,760.96 486.059,760.747 488.04,760.526 490.022,760.297 \n",
       "  492.004,760.059 493.985,759.813 495.967,759.559 497.949,759.295 499.93,759.021 501.912,758.738 503.894,758.445 505.876,758.141 507.857,757.826 509.839,757.5 \n",
       "  511.821,757.162 513.802,756.811 515.784,756.449 517.766,756.073 519.747,755.683 521.729,755.28 523.711,754.861 525.693,754.428 527.674,753.98 529.656,753.515 \n",
       "  531.638,753.033 533.619,752.534 535.601,752.017 537.583,751.481 539.564,750.926 541.546,750.351 543.528,749.755 545.509,749.137 547.491,748.498 549.473,747.835 \n",
       "  551.455,747.148 553.436,746.437 555.418,745.7 557.4,744.937 559.381,744.146 561.363,743.326 563.345,742.477 565.326,741.598 567.308,740.687 569.29,739.743 \n",
       "  571.272,738.765 573.253,737.751 575.235,736.702 577.217,735.615 579.198,734.488 581.18,733.322 583.162,732.113 585.143,730.861 587.125,729.564 589.107,728.221 \n",
       "  591.088,726.83 593.07,725.389 595.052,723.897 597.034,722.351 599.015,720.75 600.997,719.093 602.979,717.376 604.96,715.598 606.942,713.758 608.924,711.852 \n",
       "  610.905,709.879 612.887,707.836 614.869,705.722 616.85,703.533 618.832,701.268 620.814,698.923 622.796,696.496 624.777,693.985 626.759,691.387 628.741,688.7 \n",
       "  630.722,685.919 632.704,683.044 634.686,680.07 636.667,676.994 638.649,673.815 640.631,670.528 642.613,667.13 644.594,663.619 646.576,659.992 648.558,656.245 \n",
       "  650.539,652.374 652.521,648.378 654.503,644.252 656.484,639.994 658.466,635.6 660.448,631.067 662.429,626.393 664.411,621.573 666.393,616.605 668.375,611.487 \n",
       "  670.356,606.215 672.338,600.786 674.32,595.199 676.301,589.45 678.283,583.537 680.265,577.459 682.246,571.213 684.228,564.798 686.21,558.212 688.192,551.454 \n",
       "  690.173,544.523 692.155,537.419 694.137,530.141 696.118,522.69 698.1,515.067 700.082,507.271 702.063,499.306 704.045,491.172 706.027,482.872 708.008,474.409 \n",
       "  709.99,465.787 711.972,457.01 713.954,448.082 715.935,439.01 717.917,429.798 719.899,420.454 721.88,410.985 723.862,401.399 725.844,391.705 727.825,381.913 \n",
       "  729.807,372.033 731.789,362.076 733.77,352.054 735.752,341.979 737.734,331.865 739.716,321.726 741.697,311.576 743.679,301.432 745.661,291.308 747.642,281.222 \n",
       "  749.624,271.191 751.606,261.233 753.587,251.365 755.569,241.608 757.551,231.98 759.533,222.5 761.514,213.188 763.496,204.065 765.478,195.15 767.459,186.463 \n",
       "  769.441,178.024 771.423,169.853 773.404,161.97 775.386,154.394 777.368,147.144 779.349,140.239 781.331,133.695 783.313,127.531 785.295,121.763 787.276,116.405 \n",
       "  789.258,111.474 791.24,106.982 793.221,102.942 795.203,99.3646 797.185,96.2608 799.166,93.6391 801.148,91.5071 803.13,89.8707 805.112,88.7349 807.093,88.1028 \n",
       "  809.075,87.9763 811.057,88.3557 813.038,89.24 815.02,90.6265 817.002,92.5114 818.983,94.8891 820.965,97.7528 822.947,101.094 824.928,104.904 826.91,109.172 \n",
       "  828.892,113.885 830.874,119.032 832.855,124.596 834.837,130.565 836.819,136.921 838.8,143.647 840.782,150.727 842.764,158.143 844.745,165.874 846.727,173.904 \n",
       "  848.709,182.211 850.691,190.776 852.672,199.58 854.654,208.602 856.636,217.822 858.617,227.22 860.599,236.776 862.581,246.471 864.562,256.286 866.544,266.201 \n",
       "  868.526,276.198 870.507,286.259 872.489,296.366 874.471,306.502 876.453,316.651 878.434,326.797 880.416,336.926 882.398,347.022 884.379,357.072 886.361,367.063 \n",
       "  888.343,376.983 890.324,386.82 892.306,396.564 894.288,406.205 896.269,415.734 898.251,425.141 900.233,434.42 902.215,443.563 904.196,452.564 906.178,461.417 \n",
       "  908.16,470.117 910.141,478.66 912.123,487.042 914.105,495.259 916.086,503.309 918.068,511.19 920.05,518.899 922.032,526.437 924.013,533.801 925.995,540.992 \n",
       "  927.977,548.009 929.958,554.853 931.94,561.525 933.922,568.026 935.903,574.356 937.885,580.518 939.867,586.513 941.848,592.344 943.83,598.012 945.812,603.519 \n",
       "  947.794,608.869 949.775,614.064 951.757,619.107 953.739,624 955.72,628.747 957.702,633.35 959.684,637.813 961.665,642.139 963.647,646.33 965.629,650.391 \n",
       "  967.611,654.324 969.592,658.132 971.574,661.819 973.556,665.388 975.537,668.841 977.519,672.183 979.501,675.416 981.482,678.543 983.464,681.567 985.446,684.492 \n",
       "  987.427,687.319 989.409,690.053 991.391,692.695 993.373,695.249 995.354,697.718 997.336,700.103 999.318,702.408 1001.3,704.634 1003.28,706.786 1005.26,708.864 \n",
       "  1007.24,710.871 1009.23,712.81 1011.21,714.683 1013.19,716.492 1015.17,718.239 1017.15,719.925 1019.13,721.554 1021.12,723.127 1023.1,724.646 1025.08,726.112 \n",
       "  1027.06,727.528 1029.04,728.895 1031.02,730.214 1033.01,731.488 1034.99,732.718 1036.97,733.906 1038.95,735.052 1040.93,736.158 1042.91,737.226 1044.9,738.257 \n",
       "  1046.88,739.252 1048.86,740.213 1050.84,741.14 1052.82,742.035 1054.81,742.899 1056.79,743.733 1058.77,744.538 1060.75,745.315 1062.73,746.065 1064.71,746.788 \n",
       "  1066.7,747.487 1068.68,748.161 1070.66,748.812 1072.64,749.44 1074.62,750.046 1076.6,750.631 1078.59,751.196 1080.57,751.741 1082.55,752.267 1084.53,752.775 \n",
       "  1086.51,753.265 1088.49,753.738 1090.48,754.194 1092.46,754.634 1094.44,755.06 1096.42,755.47 1098.4,755.866 1100.38,756.248 1102.37,756.617 1104.35,756.973 \n",
       "  1106.33,757.316 1108.31,757.648 1110.29,757.968 1112.27,758.277 1114.26,758.575 1116.24,758.862 1118.22,759.14 1120.2,759.408 1122.18,759.666 1124.16,759.916 \n",
       "  1126.15,760.156 1128.13,760.389 1130.11,760.613 1132.09,760.829 1134.07,761.038 1136.05,761.239 1138.04,761.434 1140.02,761.621 1142,761.802 1143.98,761.977 \n",
       "  1145.96,762.146 1147.94,762.308 1149.93,762.465 1151.91,762.617 1153.89,762.763 1155.87,762.904 1157.85,763.04 1159.83,763.171 1161.82,763.297 1163.8,763.42 \n",
       "  1165.78,763.537 1167.76,763.651 1169.74,763.761 1171.73,763.866 1173.71,763.968 1175.69,764.067 1177.67,764.161 1179.65,764.253 1181.63,764.341 1183.62,764.426 \n",
       "  1185.6,764.508 1187.58,764.587 1189.56,764.663 1191.54,764.737 1193.52,764.808 1195.51,764.876 1197.49,764.942 1199.47,765.005 1201.45,765.066 1203.43,765.125 \n",
       "  1205.41,765.182 1207.4,765.236 1209.38,765.289 1211.36,765.339 1213.34,765.388 1215.32,765.435 1217.3,765.48 1219.29,765.523 1221.27,765.565 1223.25,765.605 \n",
       "  1225.23,765.644 1227.21,765.681 1229.19,765.716 1231.18,765.75 1233.16,765.783 1235.14,765.815 1237.12,765.845 1239.1,765.874 1241.08,765.901 1243.07,765.928 \n",
       "  1245.05,765.953 1247.03,765.977 1249.01,766 1250.99,766.022 1252.97,766.043 1254.96,766.063 1256.94,766.082 1258.92,766.1 1260.9,766.117 1262.88,766.133 \n",
       "  1264.86,766.149 1266.85,766.163 1268.83,766.176 1270.81,766.189 1272.79,766.201 1274.77,766.212 1276.75,766.222 1278.74,766.232 1280.72,766.24 1282.7,766.248 \n",
       "  1284.68,766.256 1286.66,766.262 1288.65,766.268 1290.63,766.273 1292.61,766.277 1294.59,766.28 1296.57,766.283 1298.55,766.285 1300.54,766.287 1302.52,766.287 \n",
       "  1304.5,766.287 1306.48,766.287 1308.46,766.285 1310.44,766.283 1312.43,766.28 1314.41,766.277 1316.39,766.273 1318.37,766.268 1320.35,766.262 1322.33,766.256 \n",
       "  1324.32,766.248 1326.3,766.24 1328.28,766.232 1330.26,766.222 1332.24,766.212 1334.22,766.201 1336.21,766.189 1338.19,766.176 1340.17,766.163 1342.15,766.149 \n",
       "  1344.13,766.133 1346.11,766.117 1348.1,766.1 1350.08,766.082 1352.06,766.063 1354.04,766.043 1356.02,766.022 1358,766 1359.99,765.977 1361.97,765.953 \n",
       "  1363.95,765.928 1365.93,765.901 1367.91,765.874 1369.89,765.845 1371.88,765.815 1373.86,765.783 1375.84,765.75 1377.82,765.716 1379.8,765.681 1381.78,765.644 \n",
       "  1383.77,765.605 1385.75,765.565 1387.73,765.523 1389.71,765.48 1391.69,765.435 1393.67,765.388 1395.66,765.339 1397.64,765.289 1399.62,765.236 1401.6,765.182 \n",
       "  1403.58,765.125 1405.57,765.066 1407.55,765.005 1409.53,764.942 1411.51,764.876 1413.49,764.808 1415.47,764.737 1417.46,764.663 1419.44,764.587 1421.42,764.508 \n",
       "  1423.4,764.426 1425.38,764.341 1427.36,764.253 1429.35,764.161 1431.33,764.067 1433.31,763.968 1435.29,763.866 1437.27,763.761 1439.25,763.651 1441.24,763.537 \n",
       "  1443.22,763.42 1445.2,763.297 1447.18,763.171 1449.16,763.04 1451.14,762.904 1453.13,762.763 1455.11,762.617 1457.09,762.465 1459.07,762.308 1461.05,762.146 \n",
       "  1463.03,761.977 1465.02,761.803 1467,761.621 1468.98,761.434 1470.96,761.239 1472.94,761.038 1474.92,760.829 1476.91,760.613 1478.89,760.389 1480.87,760.156 \n",
       "  1482.85,759.916 1484.83,759.666 1486.81,759.408 1488.8,759.14 1490.78,758.862 1492.76,758.575 1494.74,758.277 1496.72,757.968 1498.7,757.648 1500.69,757.316 \n",
       "  1502.67,756.973 1504.65,756.617 1506.63,756.248 1508.61,755.866 1510.59,755.47 1512.58,755.06 1514.56,754.635 1516.54,754.194 1518.52,753.738 1520.5,753.265 \n",
       "  1522.49,752.775 1524.47,752.267 1526.45,751.741 1528.43,751.196 1530.41,750.631 1532.39,750.046 1534.38,749.44 1536.36,748.812 1538.34,748.161 1540.32,747.487 \n",
       "  1542.3,746.789 1544.28,746.065 1546.27,745.315 1548.25,744.538 1550.23,743.733 1552.21,742.899 1554.19,742.035 1556.17,741.14 1558.16,740.213 1560.14,739.252 \n",
       "  1562.12,738.257 1564.1,737.226 1566.08,736.158 1568.06,735.052 1570.05,733.906 1572.03,732.718 1574.01,731.488 1575.99,730.214 1577.97,728.895 1579.95,727.528 \n",
       "  1581.94,726.112 1583.92,724.646 1585.9,723.127 1587.88,721.554 1589.86,719.926 1591.84,718.239 1593.83,716.492 1595.81,714.683 1597.79,712.811 1599.77,710.872 \n",
       "  1601.75,708.864 1603.73,706.786 1605.72,704.635 1607.7,702.408 1609.68,700.103 1611.66,697.718 1613.64,695.25 1615.62,692.696 1617.61,690.053 1619.59,687.32 \n",
       "  1621.57,684.492 1623.55,681.568 1625.53,678.543 1627.51,675.416 1629.5,672.183 1631.48,668.842 1633.46,665.388 1635.44,661.819 1637.42,658.132 1639.41,654.324 \n",
       "  1641.39,650.391 1643.37,646.331 1645.35,642.139 1647.33,637.813 1649.31,633.351 1651.3,628.747 1653.28,624.001 1655.26,619.107 1657.24,614.065 1659.22,608.87 \n",
       "  1661.2,603.52 1663.19,598.012 1665.17,592.344 1667.15,586.514 1669.13,580.519 1671.11,574.357 1673.09,568.027 1675.08,561.526 1677.06,554.854 1679.04,548.01 \n",
       "  1681.02,540.993 1683,533.802 1684.98,526.438 1686.97,518.9 1688.95,511.191 1690.93,503.31 1692.91,495.26 1694.89,487.043 1696.87,478.661 1698.86,470.119 \n",
       "  1700.84,461.419 1702.82,452.565 1704.8,443.565 1706.78,434.422 1708.76,425.143 1710.75,415.735 1712.73,406.207 1714.71,396.566 1716.69,386.822 1718.67,376.985 \n",
       "  1720.65,367.065 1722.64,357.074 1724.62,347.024 1726.6,336.928 1728.58,326.799 1730.56,316.653 1732.54,306.504 1734.53,296.368 1736.51,286.261 1738.49,276.2 \n",
       "  1740.47,266.203 1742.45,256.288 1744.43,246.474 1746.42,236.779 1748.4,227.222 1750.38,217.824 1752.36,208.604 1754.34,199.582 1756.33,190.779 1758.31,182.214 \n",
       "  1760.29,173.906 1762.27,165.877 1764.25,158.145 1766.23,150.73 1768.22,143.65 1770.2,136.923 1772.18,130.568 1774.16,124.599 1776.14,119.035 1778.12,113.889 \n",
       "  1780.11,109.175 1782.09,104.907 1784.07,101.098 1786.05,97.7559 1788.03,94.8922 1790.01,92.5145 1792,90.6297 1793.98,89.2431 1795.96,88.3589 1797.94,87.9794 \n",
       "  1799.92,88.1059 1801.9,88.738 1803.89,89.8739 1805.87,91.5102 1807.85,93.6422 1809.83,96.2639 1811.81,99.3677 1813.79,102.945 1815.78,106.985 1817.76,111.477 \n",
       "  1819.74,116.408 1821.72,121.766 1823.7,127.534 1825.68,133.698 1827.67,140.242 1829.65,147.147 1831.63,154.397 1833.61,161.973 1835.59,169.856 1837.57,178.027 \n",
       "  1839.56,186.466 1841.54,195.152 1843.52,204.068 1845.5,213.191 1847.48,222.502 1849.46,231.982 1851.45,241.61 1853.43,251.368 1855.41,261.235 1857.39,271.193 \n",
       "  1859.37,281.224 1861.35,291.31 1863.34,301.434 1865.32,311.578 1867.3,321.728 1869.28,331.867 1871.26,341.981 1873.25,352.056 1875.23,362.078 1877.21,372.035 \n",
       "  1879.19,381.915 1881.17,391.707 1883.15,401.401 1885.14,410.986 1887.12,420.455 1889.1,429.799 1891.08,439.011 1893.06,448.084 1895.04,457.011 1897.03,465.789 \n",
       "  1899.01,474.411 1900.99,482.873 1902.97,491.173 1904.95,499.307 1906.93,507.273 1908.92,515.068 1910.9,522.692 1912.88,530.142 1914.86,537.42 1916.84,544.524 \n",
       "  1918.82,551.455 1920.81,558.213 1922.79,564.799 1924.77,571.214 1926.75,577.46 1928.73,583.538 1930.71,589.451 1932.7,595.2 1934.68,600.787 1936.66,606.216 \n",
       "  1938.64,611.488 1940.62,616.606 1942.6,621.574 1944.59,626.393 1946.57,631.068 1948.55,635.601 1950.53,639.995 1952.51,644.253 1954.49,648.379 1956.48,652.375 \n",
       "  1958.46,656.245 1960.44,659.992 1962.42,663.62 1964.4,667.131 1966.38,670.528 1968.37,673.815 1970.35,676.995 1972.33,680.07 1974.31,683.044 1976.29,685.92 \n",
       "  1978.27,688.7 1980.26,691.388 1982.24,693.986 1984.22,696.497 1986.2,698.923 1988.18,701.268 1990.17,703.533 1992.15,705.722 1994.13,707.837 1996.11,709.879 \n",
       "  1998.09,711.852 2000.07,713.758 2002.06,715.599 2004.04,717.376 2006.02,719.093 2008,720.751 2009.98,722.351 2011.96,723.897 2013.95,725.389 2015.93,726.83 \n",
       "  2017.91,728.221 2019.89,729.565 2021.87,730.861 2023.85,732.113 2025.84,733.322 2027.82,734.489 2029.8,735.615 2031.78,736.702 2033.76,737.752 2035.74,738.765 \n",
       "  2037.73,739.743 2039.71,740.687 2041.69,741.598 2043.67,742.477 2045.65,743.326 2047.63,744.146 2049.62,744.937 2051.6,745.7 2053.58,746.437 2055.56,747.149 \n",
       "  2057.54,747.835 2059.52,748.498 2061.51,749.137 2063.49,749.755 2065.47,750.351 2067.45,750.926 2069.43,751.481 2071.41,752.017 2073.4,752.534 2075.38,753.033 \n",
       "  2077.36,753.515 2079.34,753.98 2081.32,754.428 2083.3,754.862 2085.29,755.28 2087.27,755.683 2089.25,756.073 2091.23,756.449 2093.21,756.811 2095.19,757.162 \n",
       "  2097.18,757.5 2099.16,757.826 2101.14,758.141 2103.12,758.445 2105.1,758.738 2107.09,759.022 2109.07,759.295 2111.05,759.559 2113.03,759.813 2115.01,760.059 \n",
       "  2116.99,760.297 2118.98,760.526 2120.96,760.747 2122.94,760.96 2124.92,761.166 2126.9,761.365 2128.88,761.557 2130.87,761.742 2132.85,761.921 2134.83,762.094 \n",
       "  2136.81,762.26 2138.79,762.421 2140.77,762.577 2142.76,762.727 2144.74,762.872 2146.72,763.011 2148.7,763.146 2150.68,763.277 2152.66,763.402 2154.65,763.524 \n",
       "  2156.63,763.641 2158.61,763.755 2160.59,763.864 2162.57,763.97 2164.55,764.072 2166.54,764.17 2168.52,764.265 2170.5,764.357 2172.48,764.446 2174.46,764.532 \n",
       "  2176.44,764.615 2178.43,764.695 2180.41,764.772 2182.39,764.847 2184.37,764.919 2186.35,764.989 2188.33,765.056 2190.32,765.121 2192.3,765.184 2194.28,765.245 \n",
       "  2196.26,765.304 2198.24,765.361 2200.22,765.416 2202.21,765.469 2204.19,765.521 2206.17,765.571 2208.15,765.619 2210.13,765.666 2212.12,765.711 2214.1,765.755 \n",
       "  2216.08,765.798 2218.06,765.839 2220.04,765.879 2222.02,765.917 2224.01,765.955 2225.99,765.991 2227.97,766.026 2229.95,766.061 2231.93,766.094 2233.91,766.126 \n",
       "  2235.9,766.158 2237.88,766.188 2239.86,766.218 2241.84,766.247 2243.82,766.275 2245.8,766.303 2247.79,766.33 2249.77,766.356 2251.75,766.381 2253.73,766.406 \n",
       "  2255.71,766.431 2257.69,766.454 2259.68,766.478 2261.66,766.501 2263.64,766.523 2265.62,766.545 2267.6,766.567 2269.58,766.588 2271.57,766.609 2273.55,766.63 \n",
       "  2275.53,766.65 2277.51,766.671 2279.49,766.691 2281.47,766.71 2283.46,766.73 2285.44,766.75 2287.42,766.769 2289.4,766.788 2291.38,766.807 2293.36,766.826 \n",
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       "  333.468,766.63 335.45,766.609 337.431,766.588 339.413,766.567 341.395,766.545 343.377,766.523 345.358,766.501 347.34,766.478 349.322,766.454 351.303,766.431 \n",
       "  353.285,766.406 355.267,766.381 357.248,766.356 359.23,766.33 361.212,766.303 363.194,766.275 365.175,766.247 367.157,766.218 369.139,766.188 371.12,766.158 \n",
       "  373.102,766.126 375.084,766.094 377.065,766.061 379.047,766.026 381.029,765.991 383.01,765.955 384.992,765.917 386.974,765.879 388.956,765.839 390.937,765.798 \n",
       "  392.919,765.755 394.901,765.711 396.882,765.666 398.864,765.619 400.846,765.571 402.827,765.521 404.809,765.469 406.791,765.416 408.773,765.361 410.754,765.304 \n",
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       "  670.356,606.215 672.338,600.787 674.32,595.199 676.301,589.451 678.283,583.538 680.265,577.46 682.246,571.214 684.228,564.798 686.21,558.212 688.192,551.454 \n",
       "  690.173,544.524 692.155,537.42 694.137,530.142 696.118,522.691 698.1,515.068 700.082,507.272 702.063,499.307 704.045,491.173 706.027,482.873 708.008,474.41 \n",
       "  709.99,465.788 711.972,457.011 713.954,448.083 715.935,439.011 717.917,429.799 719.899,420.455 721.88,410.986 723.862,401.4 725.844,391.706 727.825,381.914 \n",
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       "  769.441,178.026 771.423,169.855 773.404,161.972 775.386,154.397 777.368,147.147 779.349,140.241 781.331,133.698 783.313,127.533 785.295,121.765 787.276,116.408 \n",
       "  789.258,111.476 791.24,106.984 793.221,102.944 795.203,99.3669 797.185,96.2631 799.166,93.6415 801.148,91.5094 803.13,89.8731 805.112,88.7373 807.093,88.1052 \n",
       "  809.075,87.9787 811.057,88.3581 813.038,89.2424 815.02,90.629 817.002,92.5138 818.983,94.8915 820.965,97.7552 822.947,101.097 824.928,104.907 826.91,109.174 \n",
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       "  848.709,182.213 850.691,190.778 852.672,199.582 854.654,208.604 856.636,217.824 858.617,227.222 860.599,236.778 862.581,246.473 864.562,256.288 866.544,266.203 \n",
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       "  1046.88,739.258 1048.86,740.219 1050.84,741.146 1052.82,742.042 1054.81,742.906 1056.79,743.74 1058.77,744.545 1060.75,745.322 1062.73,746.072 1064.71,746.796 \n",
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       "  1264.86,766.428 1266.85,766.452 1268.83,766.476 1270.81,766.5 1272.79,766.523 1274.77,766.546 1276.75,766.568 1278.74,766.59 1280.72,766.612 1282.7,766.633 \n",
       "  1284.68,766.654 1286.66,766.675 1288.65,766.695 1290.63,766.716 1292.61,766.736 1294.59,766.756 1296.57,766.776 1298.55,766.796 1300.54,766.816 1302.52,766.836 \n",
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       "  1324.32,767.058 1326.3,767.08 1328.28,767.101 1330.26,767.123 1332.24,767.146 1334.22,767.168 1336.21,767.191 1338.19,767.215 1340.17,767.239 1342.15,767.263 \n",
       "  1344.13,767.288 1346.11,767.314 1348.1,767.34 1350.08,767.367 1352.06,767.394 1354.04,767.422 1356.02,767.451 1358,767.481 1359.99,767.511 1361.97,767.542 \n",
       "  1363.95,767.574 1365.93,767.607 1367.91,767.641 1369.89,767.676 1371.88,767.712 1373.86,767.75 1375.84,767.788 1377.82,767.827 1379.8,767.868 1381.78,767.91 \n",
       "  1383.77,767.953 1385.75,767.998 1387.73,768.044 1389.71,768.092 1391.69,768.141 1393.67,768.192 1395.66,768.245 1397.64,768.299 1399.62,768.355 1401.6,768.413 \n",
       "  1403.58,768.473 1405.57,768.535 1407.55,768.599 1409.53,768.666 1411.51,768.734 1413.49,768.806 1415.47,768.879 1417.46,768.955 1419.44,769.034 1421.42,769.115 \n",
       "  1423.4,769.2 1425.38,769.287 1427.36,769.378 1429.35,769.471 1431.33,769.568 1433.31,769.668 1435.29,769.772 1437.27,769.88 1439.25,769.991 1441.24,770.106 \n",
       "  1443.22,770.226 1445.2,770.35 1447.18,770.478 1449.16,770.61 1451.14,770.748 1453.13,770.89 1455.11,771.038 1457.09,771.19 1459.07,771.348 1461.05,771.512 \n",
       "  1463.03,771.682 1465.02,771.858 1467,772.04 1468.98,772.228 1470.96,772.424 1472.94,772.626 1474.92,772.836 1476.91,773.053 1478.89,773.278 1480.87,773.512 \n",
       "  1482.85,773.753 1484.83,774.003 1486.81,774.263 1488.8,774.531 1490.78,774.809 1492.76,775.098 1494.74,775.396 1496.72,775.706 1498.7,776.026 1500.69,776.359 \n",
       "  1502.67,776.703 1504.65,777.059 1506.63,777.428 1508.61,777.811 1510.59,778.208 1512.58,778.618 1514.56,779.044 1516.54,779.485 1518.52,779.942 1520.5,780.415 \n",
       "  1522.49,780.905 1524.47,781.414 1526.45,781.94 1528.43,782.485 1530.41,783.05 1532.39,783.636 1534.38,784.242 1536.36,784.871 1538.34,785.522 1540.32,786.196 \n",
       "  1542.3,786.895 1544.28,787.619 1546.27,788.369 1548.25,789.146 1550.23,789.951 1552.21,790.785 1554.19,791.65 1556.17,792.545 1558.16,793.472 1560.14,794.433 \n",
       "  1562.12,795.429 1564.1,796.46 1566.08,797.528 1568.06,798.635 1570.05,799.781 1572.03,800.968 1574.01,802.199 1575.99,803.473 1577.97,804.792 1579.95,806.159 \n",
       "  1581.94,807.575 1583.92,809.042 1585.9,810.561 1587.88,812.134 1589.86,813.762 1591.84,815.449 1593.83,817.196 1595.81,819.005 1597.79,820.878 1599.77,822.817 \n",
       "  1601.75,824.825 1603.73,826.903 1605.72,829.054 1607.7,831.281 1609.68,833.586 1611.66,835.971 1613.64,838.44 1615.62,840.994 1617.61,843.636 1619.59,846.37 \n",
       "  1621.57,849.198 1623.55,852.122 1625.53,855.147 1627.51,858.274 1629.5,861.507 1631.48,864.848 1633.46,868.302 1635.44,871.871 1637.42,875.558 1639.41,879.366 \n",
       "  1641.39,883.299 1643.37,887.36 1645.35,891.551 1647.33,895.877 1649.31,900.34 1651.3,904.943 1653.28,909.69 1655.26,914.584 1657.24,919.626 1659.22,924.821 \n",
       "  1661.2,930.171 1663.19,935.679 1665.17,941.347 1667.15,947.177 1669.13,953.172 1671.11,959.334 1673.09,965.665 1675.08,972.165 1677.06,978.837 1679.04,985.682 \n",
       "  1681.02,992.699 1683,999.89 1684.98,1007.25 1686.97,1014.79 1688.95,1022.5 1690.93,1030.38 1692.91,1038.43 1694.89,1046.65 1696.87,1055.03 1698.86,1063.57 \n",
       "  1700.84,1072.27 1702.82,1081.13 1704.8,1090.13 1706.78,1099.27 1708.76,1108.55 1710.75,1117.96 1712.73,1127.49 1714.71,1137.13 1716.69,1146.87 1718.67,1156.71 \n",
       "  1720.65,1166.63 1722.64,1176.62 1724.62,1186.67 1726.6,1196.77 1728.58,1206.89 1730.56,1217.04 1732.54,1227.19 1734.53,1237.33 1736.51,1247.43 1738.49,1257.49 \n",
       "  1740.47,1267.49 1742.45,1277.41 1744.43,1287.22 1746.42,1296.92 1748.4,1306.47 1750.38,1315.87 1752.36,1325.09 1754.34,1334.11 1756.33,1342.92 1758.31,1351.48 \n",
       "  1760.29,1359.79 1762.27,1367.82 1764.25,1375.55 1766.23,1382.96 1768.22,1390.04 1770.2,1396.77 1772.18,1403.13 1774.16,1409.1 1776.14,1414.66 1778.12,1419.81 \n",
       "  1780.11,1424.52 1782.09,1428.79 1784.07,1432.6 1786.05,1435.94 1788.03,1438.8 1790.01,1441.18 1792,1443.07 1793.98,1444.45 1795.96,1445.34 1797.94,1445.72 \n",
       "  1799.92,1445.59 1801.9,1444.96 1803.89,1443.82 1805.87,1442.18 1807.85,1440.05 1809.83,1437.43 1811.81,1434.33 1813.79,1430.75 1815.78,1426.71 1817.76,1422.22 \n",
       "  1819.74,1417.29 1821.72,1411.93 1823.7,1406.16 1825.68,1400 1827.67,1393.45 1829.65,1386.55 1831.63,1379.3 1833.61,1371.72 1835.59,1363.84 1837.57,1355.67 \n",
       "  1839.56,1347.23 1841.54,1338.54 1843.52,1329.63 1845.5,1320.5 1847.48,1311.19 1849.46,1301.71 1851.45,1292.08 1853.43,1282.33 1855.41,1272.46 1857.39,1262.5 \n",
       "  1859.37,1252.47 1861.35,1242.38 1863.34,1232.26 1865.32,1222.12 1867.3,1211.97 1869.28,1201.83 1871.26,1191.71 1873.25,1181.64 1875.23,1171.62 1877.21,1161.66 \n",
       "  1879.19,1151.78 1881.17,1141.99 1883.15,1132.29 1885.14,1122.71 1887.12,1113.24 1889.1,1103.89 1891.08,1094.68 1893.06,1085.61 1895.04,1076.68 1897.03,1067.9 \n",
       "  1899.01,1059.28 1900.99,1050.82 1902.97,1042.52 1904.95,1034.39 1906.93,1026.42 1908.92,1018.62 1910.9,1011 1912.88,1003.55 1914.86,996.273 1916.84,989.169 \n",
       "  1918.82,982.238 1920.81,975.48 1922.79,968.894 1924.77,962.478 1926.75,956.232 1928.73,950.154 1930.71,944.242 1932.7,938.493 1934.68,932.905 1936.66,927.477 \n",
       "  1938.64,922.205 1940.62,917.086 1942.6,912.118 1944.59,907.299 1946.57,902.624 1948.55,898.091 1950.53,893.697 1952.51,889.439 1954.49,885.313 1956.48,881.317 \n",
       "  1958.46,877.447 1960.44,873.7 1962.42,870.072 1964.4,866.561 1966.38,863.164 1968.37,859.877 1970.35,856.697 1972.33,853.622 1974.31,850.648 1976.29,847.772 \n",
       "  1978.27,844.992 1980.26,842.304 1982.24,839.706 1984.22,837.195 1986.2,834.769 1988.18,832.424 1990.17,830.158 1992.15,827.969 1994.13,825.855 1996.11,823.812 \n",
       "  1998.09,821.839 2000.07,819.933 2002.06,818.093 2004.04,816.315 2006.02,814.599 2008,812.941 2009.98,811.34 2011.96,809.795 2013.95,808.302 2015.93,806.861 \n",
       "  2017.91,805.47 2019.89,804.127 2021.87,802.83 2023.85,801.578 2025.84,800.37 2027.82,799.203 2029.8,798.077 2031.78,796.989 2033.76,795.94 2035.74,794.927 \n",
       "  2037.73,793.949 2039.71,793.005 2041.69,792.094 2043.67,791.214 2045.65,790.365 2047.63,789.545 2049.62,788.754 2051.6,787.991 2053.58,787.254 2055.56,786.543 \n",
       "  2057.54,785.856 2059.52,785.194 2061.51,784.554 2063.49,783.937 2065.47,783.341 2067.45,782.766 2069.43,782.211 2071.41,781.675 2073.4,781.158 2075.38,780.658 \n",
       "  2077.36,780.177 2079.34,779.712 2081.32,779.263 2083.3,778.83 2085.29,778.412 2087.27,778.008 2089.25,777.619 2091.23,777.243 2093.21,776.88 2095.19,776.53 \n",
       "  2097.18,776.192 2099.16,775.865 2101.14,775.55 2103.12,775.246 2105.1,774.953 2107.09,774.67 2109.07,774.396 2111.05,774.133 2113.03,773.878 2115.01,773.632 \n",
       "  2116.99,773.395 2118.98,773.166 2120.96,772.945 2122.94,772.731 2124.92,772.525 2126.9,772.326 2128.88,772.134 2130.87,771.949 2132.85,771.77 2134.83,771.597 \n",
       "  2136.81,771.431 2138.79,771.27 2140.77,771.114 2142.76,770.965 2144.74,770.82 2146.72,770.68 2148.7,770.545 2150.68,770.415 2152.66,770.289 2154.65,770.167 \n",
       "  2156.63,770.05 2158.61,769.937 2160.59,769.827 2162.57,769.722 2164.55,769.62 2166.54,769.521 2168.52,769.426 2170.5,769.334 2172.48,769.245 2174.46,769.16 \n",
       "  2176.44,769.077 2178.43,768.997 2180.41,768.919 2182.39,768.845 2184.37,768.772 2186.35,768.703 2188.33,768.635 2190.32,768.57 2192.3,768.507 2194.28,768.446 \n",
       "  2196.26,768.387 2198.24,768.33 2200.22,768.275 2202.21,768.222 2204.19,768.17 2206.17,768.12 2208.15,768.072 2210.13,768.025 2212.12,767.98 2214.1,767.936 \n",
       "  2216.08,767.894 2218.06,767.852 2220.04,767.813 2222.02,767.774 2224.01,767.736 2225.99,767.7 2227.97,767.665 2229.95,767.63 2231.93,767.597 2233.91,767.565 \n",
       "  2235.9,767.533 2237.88,767.503 2239.86,767.473 2241.84,767.444 2243.82,767.416 2245.8,767.388 2247.79,767.362 2249.77,767.336 2251.75,767.31 2253.73,767.285 \n",
       "  2255.71,767.261 2257.69,767.237 2259.68,767.213 2261.66,767.191 2263.64,767.168 2265.62,767.146 2267.6,767.124 2269.58,767.103 2271.57,767.082 2273.55,767.061 \n",
       "  2275.53,767.041 2277.51,767.021 2279.49,767.001 2281.47,766.981 2283.46,766.961 2285.44,766.942 2287.42,766.922 2289.4,766.903 2291.38,766.884 2293.36,766.865 \n",
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      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "plot(xvec,[mat_v2[:,1:2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "これは、いわゆる「結合性軌道」と「反結合性軌道」となっている。\n",
    "\n",
    "#### 1.1.3 ポテンシャルを二つ持つ場合の束縛状態:近づけた場合\n",
    "さらに近づけるとどうなるだろうか？  \n",
    "ポテンシャルを"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "  877.449,1042.56 879.53,1065.12 881.611,1087.43 883.692,1109.42 885.773,1131.05 887.854,1152.29 889.934,1173.1 892.015,1193.42 894.096,1213.23 896.177,1232.47 \n",
       "  898.258,1251.1 900.339,1269.1 902.42,1286.41 904.501,1302.99 906.582,1318.83 908.663,1333.87 910.744,1348.08 912.825,1361.43 914.905,1373.89 916.986,1385.44 \n",
       "  919.067,1396.04 921.148,1405.67 923.229,1414.3 925.31,1421.93 927.391,1428.52 929.472,1434.07 931.553,1438.55 933.634,1441.97 935.715,1444.3 937.796,1445.55 \n",
       "  939.876,1445.72 941.957,1444.79 944.038,1442.78 946.119,1439.69 948.2,1435.52 950.281,1430.29 952.362,1424.01 954.443,1416.7 956.524,1408.36 958.605,1399.03 \n",
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       "  981.495,1238.12 983.576,1219.06 985.657,1199.42 987.738,1179.25 989.818,1158.58 991.899,1137.47 993.98,1115.95 996.061,1094.06 998.142,1071.85 1000.22,1049.35 \n",
       "  1002.3,1026.62 1004.38,1003.69 1006.47,980.612 1008.55,957.413 1010.63,934.139 1012.71,910.827 1014.79,887.517 1016.87,864.245 1018.95,841.046 1021.03,817.955 \n",
       "  1023.11,795.006 1025.19,772.228 1027.27,749.655 1029.36,727.313 1031.44,705.23 1033.52,683.433 1035.6,661.945 1037.68,640.789 1039.76,619.987 1041.84,599.557 \n",
       "  1043.92,579.517 1046,559.884 1048.08,540.672 1050.17,521.895 1052.25,503.562 1054.33,485.686 1056.41,468.273 1058.49,451.332 1060.57,434.867 1062.65,418.882 \n",
       "  1064.73,403.382 1066.81,388.366 1068.89,373.836 1070.97,359.791 1073.06,346.229 1075.14,333.147 1077.22,320.541 1079.3,308.407 1081.38,296.738 1083.46,285.529 \n",
       "  1085.54,274.771 1087.62,264.458 1089.7,254.581 1091.78,245.13 1093.86,236.097 1095.95,227.471 1098.03,219.242 1100.11,211.4 1102.19,203.933 1104.27,196.831 \n",
       "  1106.35,190.082 1108.43,183.674 1110.51,177.597 1112.59,171.838 1114.67,166.387 1116.75,161.231 1118.84,156.359 1120.92,151.76 1123,147.423 1125.08,143.336 \n",
       "  1127.16,139.489 1129.24,135.871 1131.32,132.472 1133.4,129.28 1135.48,126.287 1137.56,123.482 1139.64,120.856 1141.73,118.4 1143.81,116.105 1145.89,113.962 \n",
       "  1147.97,111.963 1150.05,110.101 1152.13,108.366 1154.21,106.753 1156.29,105.253 1158.37,103.86 1160.45,102.568 1162.53,101.37 1164.62,100.261 1166.7,99.2349 \n",
       "  1168.78,98.2861 1170.86,97.4097 1172.94,96.6009 1175.02,95.8553 1177.1,95.1683 1179.18,94.5361 1181.26,93.9548 1183.34,93.4207 1185.42,92.9305 1187.51,92.4809 \n",
       "  1189.59,92.069 1191.67,91.692 1193.75,91.3472 1195.83,91.0321 1197.91,90.7446 1199.99,90.4825 1202.07,90.2437 1204.15,90.0264 1206.23,89.829 1208.31,89.6497 \n",
       "  1210.4,89.4873 1212.48,89.3402 1214.56,89.2072 1216.64,89.0873 1218.72,88.9793 1220.8,88.8823 1222.88,88.7954 1224.96,88.7178 1227.04,88.6487 1229.12,88.5876 \n",
       "  1231.2,88.5338 1233.29,88.4868 1235.37,88.4461 1237.45,88.4114 1239.53,88.3823 1241.61,88.3585 1243.69,88.3397 1245.77,88.3258 1247.85,88.3166 1249.93,88.312 \n",
       "  1252.01,88.312 1254.09,88.3166 1256.18,88.3258 1258.26,88.3397 1260.34,88.3585 1262.42,88.3823 1264.5,88.4114 1266.58,88.4461 1268.66,88.4868 1270.74,88.5338 \n",
       "  1272.82,88.5876 1274.9,88.6487 1276.98,88.7178 1279.07,88.7954 1281.15,88.8823 1283.23,88.9793 1285.31,89.0873 1287.39,89.2072 1289.47,89.3402 1291.55,89.4873 \n",
       "  1293.63,89.6497 1295.71,89.829 1297.79,90.0264 1299.87,90.2437 1301.96,90.4825 1304.04,90.7446 1306.12,91.0321 1308.2,91.3472 1310.28,91.692 1312.36,92.069 \n",
       "  1314.44,92.4809 1316.52,92.9305 1318.6,93.4207 1320.68,93.9548 1322.76,94.5361 1324.85,95.1683 1326.93,95.8553 1329.01,96.6009 1331.09,97.4097 1333.17,98.2861 \n",
       "  1335.25,99.2349 1337.33,100.261 1339.41,101.37 1341.49,102.568 1343.57,103.86 1345.66,105.253 1347.74,106.753 1349.82,108.366 1351.9,110.101 1353.98,111.963 \n",
       "  1356.06,113.962 1358.14,116.105 1360.22,118.4 1362.3,120.856 1364.38,123.482 1366.46,126.287 1368.55,129.28 1370.63,132.472 1372.71,135.871 1374.79,139.489 \n",
       "  1376.87,143.336 1378.95,147.423 1381.03,151.76 1383.11,156.359 1385.19,161.231 1387.27,166.387 1389.35,171.838 1391.44,177.597 1393.52,183.674 1395.6,190.082 \n",
       "  1397.68,196.831 1399.76,203.933 1401.84,211.4 1403.92,219.242 1406,227.471 1408.08,236.097 1410.16,245.13 1412.24,254.581 1414.33,264.458 1416.41,274.771 \n",
       "  1418.49,285.529 1420.57,296.738 1422.65,308.407 1424.73,320.541 1426.81,333.147 1428.89,346.229 1430.97,359.791 1433.05,373.836 1435.13,388.366 1437.22,403.382 \n",
       "  1439.3,418.882 1441.38,434.867 1443.46,451.332 1445.54,468.273 1447.62,485.686 1449.7,503.562 1451.78,521.895 1453.86,540.672 1455.94,559.884 1458.02,579.517 \n",
       "  1460.11,599.557 1462.19,619.987 1464.27,640.789 1466.35,661.945 1468.43,683.433 1470.51,705.23 1472.59,727.313 1474.67,749.655 1476.75,772.228 1478.83,795.006 \n",
       "  1480.91,817.955 1483,841.046 1485.08,864.245 1487.16,887.517 1489.24,910.827 1491.32,934.139 1493.4,957.413 1495.48,980.612 1497.56,1003.69 1499.64,1026.62 \n",
       "  1501.72,1049.35 1503.8,1071.85 1505.89,1094.06 1507.97,1115.95 1510.05,1137.47 1512.13,1158.58 1514.21,1179.25 1516.29,1199.42 1518.37,1219.06 1520.45,1238.12 \n",
       "  1522.53,1256.57 1524.61,1274.36 1526.69,1291.46 1528.78,1307.83 1530.86,1323.42 1532.94,1338.22 1535.02,1352.17 1537.1,1365.26 1539.18,1377.45 1541.26,1388.72 \n",
       "  1543.34,1399.03 1545.42,1408.36 1547.5,1416.7 1549.58,1424.01 1551.67,1430.29 1553.75,1435.52 1555.83,1439.69 1557.91,1442.78 1559.99,1444.79 1562.07,1445.72 \n",
       "  1564.15,1445.55 1566.23,1444.3 1568.31,1441.97 1570.39,1438.55 1572.47,1434.07 1574.56,1428.52 1576.64,1421.93 1578.72,1414.3 1580.8,1405.67 1582.88,1396.04 \n",
       "  1584.96,1385.44 1587.04,1373.89 1589.12,1361.43 1591.2,1348.08 1593.28,1333.87 1595.36,1318.83 1597.45,1302.99 1599.53,1286.41 1601.61,1269.1 1603.69,1251.1 \n",
       "  1605.77,1232.47 1607.85,1213.23 1609.93,1193.42 1612.01,1173.1 1614.09,1152.29 1616.17,1131.05 1618.26,1109.42 1620.34,1087.43 1622.42,1065.12 1624.5,1042.56 \n",
       "  1626.58,1019.76 1628.66,996.784 1630.74,973.662 1632.82,950.437 1634.9,927.147 1636.98,903.833 1639.06,880.53 1641.15,857.276 1643.23,834.106 1645.31,811.054 \n",
       "  1647.39,788.153 1649.47,765.434 1651.55,742.926 1653.63,720.66 1655.71,698.66 1657.79,676.953 1659.87,655.563 1661.95,634.511 1664.04,613.818 1666.12,593.503 \n",
       "  1668.2,573.584 1670.28,554.076 1672.36,534.993 1674.44,516.348 1676.52,498.151 1678.6,480.413 1680.68,463.141 1682.76,446.342 1684.84,430.021 1686.93,414.181 \n",
       "  1689.01,398.826 1691.09,383.956 1693.17,369.572 1695.25,355.672 1697.33,342.254 1699.41,329.315 1701.49,316.852 1703.57,304.857 1705.65,293.327 1707.73,282.254 \n",
       "  1709.82,271.631 1711.9,261.45 1713.98,251.701 1716.06,242.377 1718.14,233.467 1720.22,224.961 1722.3,216.85 1724.38,209.121 1726.46,201.765 1728.54,194.769 \n",
       "  1730.62,188.124 1732.71,181.817 1734.79,175.836 1736.87,170.171 1738.95,164.809 1741.03,159.74 1743.11,154.951 1745.19,150.432 1747.27,146.171 1749.35,142.158 \n",
       "  1751.43,138.38 1753.51,134.829 1755.6,131.493 1757.68,128.362 1759.76,125.426 1761.84,122.676 1763.92,120.102 1766,117.695 1768.08,115.446 1770.16,113.348 \n",
       "  1772.24,111.39 1774.32,109.567 1776.4,107.869 1778.49,106.291 1780.57,104.824 1782.65,103.462 1784.73,102.199 1786.81,101.028 1788.89,99.9443 1790.97,98.9417 \n",
       "  1793.05,98.015 1795.13,97.1592 1797.21,96.3697 1799.29,95.6419 1801.38,94.9716 1803.46,94.3548 1805.54,93.7878 1807.62,93.2669 1809.7,92.7888 1811.78,92.3504 \n",
       "  1813.86,91.9488 1815.94,91.5811 1818.02,91.2449 1820.1,90.9376 1822.18,90.6571 1824.27,90.4012 1826.35,90.168 1828.43,89.9556 1830.51,89.7624 1832.59,89.5867 \n",
       "  1834.67,89.4272 1836.75,89.2824 1838.83,89.1511 1840.91,89.0322 1842.99,88.9245 1845.07,88.8272 1847.16,88.7392 1849.24,88.6598 1851.32,88.5881 1853.4,88.5235 \n",
       "  1855.48,88.4654 1857.56,88.4131 1859.64,88.366 1861.72,88.3238 1863.8,88.2858 1865.88,88.2518 1867.96,88.2214 1870.05,88.1941 1872.13,88.1697 1874.21,88.1479 \n",
       "  1876.29,88.1285 1878.37,88.1111 1880.45,88.0956 1882.53,88.0818 1884.61,88.0696 1886.69,88.0586 1888.77,88.049 1890.86,88.0404 1892.94,88.0327 1895.02,88.026 \n",
       "  1897.1,88.02 1899.18,88.0147 1901.26,88.01 1903.34,88.0059 1905.42,88.0022 1907.5,87.999 1909.58,87.9962 1911.66,87.9937 1913.75,87.9915 1915.83,87.9896 \n",
       "  1917.91,87.9879 1919.99,87.9864 1922.07,87.9851 1924.15,87.9839 1926.23,87.9829 1928.31,87.9821 1930.39,87.9813 1932.47,87.9806 1934.55,87.9801 1936.64,87.9796 \n",
       "  1938.72,87.9791 1940.8,87.9787 1942.88,87.9784 1944.96,87.9781 1947.04,87.9779 1949.12,87.9776 1951.2,87.9774 1953.28,87.9773 1955.36,87.9771 1957.44,87.977 \n",
       "  1959.53,87.9769 1961.61,87.9768 1963.69,87.9767 1965.77,87.9767 1967.85,87.9766 1969.93,87.9766 1972.01,87.9765 1974.09,87.9765 1976.17,87.9765 1978.25,87.9764 \n",
       "  1980.33,87.9764 1982.42,87.9764 1984.5,87.9764 1986.58,87.9764 1988.66,87.9763 1990.74,87.9763 1992.82,87.9763 1994.9,87.9763 1996.98,87.9763 1999.06,87.9763 \n",
       "  2001.14,87.9763 2003.22,87.9763 2005.31,87.9763 2007.39,87.9763 2009.47,87.9763 2011.55,87.9763 2013.63,87.9763 2015.71,87.9763 2017.79,87.9763 2019.87,87.9763 \n",
       "  2021.95,87.9763 2024.03,87.9763 2026.11,87.9763 2028.2,87.9763 2030.28,87.9763 2032.36,87.9763 2034.44,87.9763 2036.52,87.9763 2038.6,87.9763 2040.68,87.9763 \n",
       "  2042.76,87.9763 2044.84,87.9763 2046.92,87.9763 2049,87.9763 2051.09,87.9763 2053.17,87.9763 2055.25,87.9763 2057.33,87.9763 2059.41,87.9763 2061.49,87.9763 \n",
       "  2063.57,87.9763 2065.65,87.9763 2067.73,87.9763 2069.81,87.9763 2071.89,87.9763 2073.98,87.9763 2076.06,87.9763 2078.14,87.9763 2080.22,87.9763 2082.3,87.9763 \n",
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      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V0 = -5.0\n",
    "x0 = 3\n",
    "N = 1000\n",
    "xmax = 10.0\n",
    "xmin = -10.0\n",
    "xvec = range(xmin,xmax,length=N)\n",
    "V2(x) =  V0*(exp(-(x-x0)^2)+exp(-(x+x0)^2))\n",
    "plot(xvec,V2.(xvec),label=\"Potential\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "として、エネルギーを計算してみると、"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ポテンシャル二つの時のエネルギー\n",
      "[-3.140920983555882, -3.1398815968014215, -0.44595025974323477, -0.3552571780425424, 0.23882591948532816, 0.3086787489395739, 0.6213904023194616, 0.976257854228817, 1.2742974105308358, 1.7696233897102687]\n",
      "ポテンシャル一つの時のエネルギー\n",
      "[-3.1404009040145286, -0.4062142205546486, 0.10339356506001751, 0.15632796480264988, 0.4145932097452478, 0.5822287366538306, 0.9363743175283377, 1.2355092013437883, 1.6711811288154879, 2.0989689480359477]\n"
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       "  1423.4,683.647 1425.38,680.772 1427.36,677.797 1429.35,674.718 1431.33,671.532 1433.31,668.237 1435.29,664.828 1437.27,661.304 1439.25,657.661 1441.24,653.897 \n",
       "  1443.22,650.006 1445.2,645.988 1447.18,641.838 1449.16,637.554 1451.14,633.132 1453.13,628.569 1455.11,623.862 1457.09,619.008 1459.07,614.005 1461.05,608.849 \n",
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       "  1482.85,541.382 1484.83,534.227 1486.81,526.898 1488.8,519.396 1490.78,511.721 1492.76,503.875 1494.74,495.859 1496.72,487.676 1498.7,479.327 1500.69,470.817 \n",
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       "  1681.02,381.276 1683,391.07 1684.98,400.767 1686.97,410.356 1688.95,419.83 1690.93,429.179 1692.91,438.397 1694.89,447.477 1696.87,456.412 1698.86,465.198 \n",
       "  1700.84,473.828 1702.82,482.3 1704.8,490.609 1706.78,498.753 1708.76,506.729 1710.75,514.535 1712.73,522.169 1714.71,529.631 1716.69,536.92 1718.67,544.035 \n",
       "  1720.65,550.977 1722.64,557.746 1724.62,564.344 1726.6,570.771 1728.58,577.028 1730.56,583.117 1732.54,589.041 1734.53,594.801 1736.51,600.4 1738.49,605.839 \n",
       "  1740.47,611.122 1742.45,616.251 1744.43,621.229 1746.42,626.059 1748.4,630.743 1750.38,635.286 1752.36,639.69 1754.34,643.957 1756.33,648.092 1758.31,652.098 \n",
       "  1760.29,655.977 1762.27,659.733 1764.25,663.368 1766.23,666.887 1768.22,670.293 1770.2,673.587 1772.18,676.775 1774.16,679.857 1776.14,682.838 1778.12,685.721 \n",
       "  1780.11,688.508 1782.09,691.202 1784.07,693.807 1786.05,696.324 1788.03,698.756 1790.01,701.106 1792,703.377 1793.98,705.572 1795.96,707.691 1797.94,709.739 \n",
       "  1799.92,711.717 1801.9,713.627 1803.89,715.472 1805.87,717.254 1807.85,718.975 1809.83,720.637 1811.81,722.241 1813.79,723.791 1815.78,725.287 1817.76,726.731 \n",
       "  1819.74,728.126 1821.72,729.472 1823.7,730.772 1825.68,732.027 1827.67,733.239 1829.65,734.408 1831.63,735.537 1833.61,736.627 1835.59,737.679 1837.57,738.695 \n",
       "  1839.56,739.675 1841.54,740.621 1843.52,741.535 1845.5,742.416 1847.48,743.267 1849.46,744.089 1851.45,744.882 1853.43,745.647 1855.41,746.385 1857.39,747.098 \n",
       "  1859.37,747.786 1861.35,748.451 1863.34,749.092 1865.32,749.71 1867.3,750.307 1869.28,750.884 1871.26,751.44 1873.25,751.977 1875.23,752.495 1877.21,752.995 \n",
       "  1879.19,753.478 1881.17,753.944 1883.15,754.394 1885.14,754.828 1887.12,755.247 1889.1,755.651 1891.08,756.041 1893.06,756.418 1895.04,756.781 1897.03,757.132 \n",
       "  1899.01,757.471 1900.99,757.797 1902.97,758.113 1904.95,758.417 1906.93,758.711 1908.92,758.995 1910.9,759.268 1912.88,759.532 1914.86,759.787 1916.84,760.033 \n",
       "  1918.82,760.271 1920.81,760.5 1922.79,760.721 1924.77,760.935 1926.75,761.141 1928.73,761.34 1930.71,761.532 1932.7,761.717 1934.68,761.896 1936.66,762.068 \n",
       "  1938.64,762.235 1940.62,762.395 1942.6,762.551 1944.59,762.7 1946.57,762.845 1948.55,762.984 1950.53,763.119 1952.51,763.249 1954.49,763.374 1956.48,763.495 \n",
       "  1958.46,763.612 1960.44,763.725 1962.42,763.834 1964.4,763.939 1966.38,764.04 1968.37,764.138 1970.35,764.232 1972.33,764.323 1974.31,764.411 1976.29,764.496 \n",
       "  1978.27,764.578 1980.26,764.657 1982.24,764.733 1984.22,764.807 1986.2,764.878 1988.18,764.947 1990.17,765.013 1992.15,765.077 1994.13,765.138 1996.11,765.198 \n",
       "  1998.09,765.255 2000.07,765.311 2002.06,765.364 2004.04,765.416 2006.02,765.466 2008,765.514 2009.98,765.56 2011.96,765.605 2013.95,765.648 2015.93,765.69 \n",
       "  2017.91,765.73 2019.89,765.769 2021.87,765.807 2023.85,765.843 2025.84,765.878 2027.82,765.912 2029.8,765.944 2031.78,765.976 2033.76,766.006 2035.74,766.035 \n",
       "  2037.73,766.064 2039.71,766.091 2041.69,766.117 2043.67,766.143 2045.65,766.167 2047.63,766.191 2049.62,766.214 2051.6,766.236 2053.58,766.257 2055.56,766.278 \n",
       "  2057.54,766.297 2059.52,766.317 2061.51,766.335 2063.49,766.353 2065.47,766.37 2067.45,766.387 2069.43,766.403 2071.41,766.418 2073.4,766.433 2075.38,766.447 \n",
       "  2077.36,766.461 2079.34,766.475 2081.32,766.488 2083.3,766.5 2085.29,766.512 2087.27,766.524 2089.25,766.535 2091.23,766.546 2093.21,766.556 2095.19,766.567 \n",
       "  2097.18,766.576 2099.16,766.586 2101.14,766.595 2103.12,766.604 2105.1,766.612 2107.09,766.62 2109.07,766.628 2111.05,766.636 2113.03,766.643 2115.01,766.65 \n",
       "  2116.99,766.657 2118.98,766.664 2120.96,766.67 2122.94,766.676 2124.92,766.682 2126.9,766.688 2128.88,766.693 2130.87,766.699 2132.85,766.704 2134.83,766.709 \n",
       "  2136.81,766.714 2138.79,766.718 2140.77,766.723 2142.76,766.727 2144.74,766.731 2146.72,766.735 2148.7,766.739 2150.68,766.743 2152.66,766.747 2154.65,766.75 \n",
       "  2156.63,766.754 2158.61,766.757 2160.59,766.76 2162.57,766.763 2164.55,766.766 2166.54,766.769 2168.52,766.772 2170.5,766.774 2172.48,766.777 2174.46,766.779 \n",
       "  2176.44,766.782 2178.43,766.784 2180.41,766.786 2182.39,766.788 2184.37,766.79 2186.35,766.792 2188.33,766.794 2190.32,766.796 2192.3,766.798 2194.28,766.8 \n",
       "  2196.26,766.802 2198.24,766.803 2200.22,766.805 2202.21,766.806 2204.19,766.808 2206.17,766.809 2208.15,766.811 2210.13,766.812 2212.12,766.813 2214.1,766.815 \n",
       "  2216.08,766.816 2218.06,766.817 2220.04,766.818 2222.02,766.819 2224.01,766.82 2225.99,766.821 2227.97,766.822 2229.95,766.823 2231.93,766.824 2233.91,766.825 \n",
       "  2235.9,766.826 2237.88,766.827 2239.86,766.828 2241.84,766.829 2243.82,766.83 2245.8,766.83 2247.79,766.831 2249.77,766.832 2251.75,766.833 2253.73,766.833 \n",
       "  2255.71,766.834 2257.69,766.835 2259.68,766.835 2261.66,766.836 2263.64,766.837 2265.62,766.837 2267.6,766.838 2269.58,766.839 2271.57,766.839 2273.55,766.84 \n",
       "  2275.53,766.84 2277.51,766.841 2279.49,766.842 2281.47,766.842 2283.46,766.843 2285.44,766.843 2287.42,766.844 2289.4,766.844 2291.38,766.845 2293.36,766.845 \n",
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       "  1284.68,773.472 1286.66,772.752 1288.65,772.04 1290.63,771.334 1292.61,770.634 1294.59,769.939 1296.57,769.248 1298.55,768.559 1300.54,767.873 1302.52,767.188 \n",
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       "  1363.95,741.659 1365.93,740.518 1367.91,739.345 1369.89,738.137 1371.88,736.893 1373.86,735.612 1375.84,734.292 1377.82,732.931 1379.8,731.528 1381.78,730.081 \n",
       "  1383.77,728.589 1385.75,727.048 1387.73,725.459 1389.71,723.818 1391.69,722.124 1393.67,720.375 1395.66,718.568 1397.64,716.702 1399.62,714.775 1401.6,712.784 \n",
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       "  1423.4,685.968 1425.38,683.015 1427.36,679.964 1429.35,676.812 1431.33,673.556 1433.31,670.192 1435.29,666.718 1437.27,663.13 1439.25,659.426 1441.24,655.601 \n",
       "  1443.22,651.653 1445.2,647.579 1447.18,643.375 1449.16,639.038 1451.14,634.565 1453.13,629.953 1455.11,625.199 1457.09,620.299 1459.07,615.251 1461.05,610.051 \n",
       "  1463.03,604.697 1465.02,599.187 1467,593.517 1468.98,587.685 1470.96,581.69 1472.94,575.528 1474.92,569.199 1476.91,562.7 1478.89,556.031 1480.87,549.189 \n",
       "  1482.85,542.175 1484.83,534.988 1486.81,527.628 1488.8,520.095 1490.78,512.39 1492.76,504.514 1494.74,496.47 1496.72,488.257 1498.7,479.881 1500.69,471.343 \n",
       "  1502.67,462.648 1504.65,453.799 1506.63,444.803 1508.61,435.663 1510.59,426.388 1512.58,416.983 1514.56,407.457 1516.54,397.818 1518.52,388.075 1520.5,378.237 \n",
       "  1522.49,368.316 1524.47,358.323 1526.45,348.27 1528.43,338.169 1530.41,328.035 1532.39,317.882 1534.38,307.724 1536.36,297.578 1538.34,287.459 1540.32,277.385 \n",
       "  1542.3,267.373 1544.28,257.441 1546.27,247.608 1548.25,237.892 1550.23,228.313 1552.21,218.891 1554.19,209.645 1556.17,200.595 1558.16,191.762 1560.14,183.164 \n",
       "  1562.12,174.823 1564.1,166.759 1566.08,158.989 1568.06,151.534 1570.05,144.413 1572.03,137.644 1574.01,131.243 1575.99,125.229 1577.97,119.617 1579.95,114.422 \n",
       "  1581.94,109.658 1583.92,105.34 1585.9,101.477 1587.88,98.0827 1589.86,95.165 1591.84,92.7328 1593.83,90.793 1595.81,89.3511 1597.79,88.4113 1599.77,87.9763 \n",
       "  1601.75,88.0473 1603.73,88.6242 1605.72,89.7053 1607.7,91.2874 1609.68,93.3659 1611.66,95.9349 1613.64,98.9869 1615.62,102.513 1617.61,106.504 1619.59,110.948 \n",
       "  1621.57,115.833 1623.55,121.146 1625.53,126.871 1627.51,132.994 1629.5,139.497 1631.48,146.365 1633.46,153.58 1635.44,161.122 1637.42,168.973 1639.41,177.114 \n",
       "  1641.39,185.526 1643.37,194.187 1645.35,203.079 1647.33,212.182 1649.31,221.475 1651.3,230.938 1653.28,240.551 1655.26,250.296 1657.24,260.153 1659.22,270.103 \n",
       "  1661.2,280.127 1663.19,290.209 1665.17,300.329 1667.15,310.473 1669.13,320.623 1671.11,330.764 1673.09,340.882 1675.08,350.962 1677.06,360.99 1679.04,370.955 \n",
       "  1681.02,380.844 1683,390.646 1684.98,400.351 1686.97,409.949 1688.95,419.431 1690.93,428.789 1692.91,438.016 1694.89,447.104 1696.87,456.047 1698.86,464.841 \n",
       "  1700.84,473.48 1702.82,481.96 1704.8,490.278 1706.78,498.429 1708.76,506.413 1710.75,514.227 1712.73,521.869 1714.71,529.339 1716.69,536.635 1718.67,543.757 \n",
       "  1720.65,550.707 1722.64,557.483 1724.62,564.088 1726.6,570.521 1728.58,576.786 1730.56,582.882 1732.54,588.812 1734.53,594.578 1736.51,600.183 1738.49,605.629 \n",
       "  1740.47,610.917 1742.45,616.052 1744.43,621.036 1746.42,625.871 1748.4,630.561 1750.38,635.109 1752.36,639.518 1754.34,643.791 1756.33,647.931 1758.31,651.941 \n",
       "  1760.29,655.824 1762.27,659.585 1764.25,663.225 1766.23,666.748 1768.22,670.158 1770.2,673.457 1772.18,676.648 1774.16,679.734 1776.14,682.719 1778.12,685.605 \n",
       "  1780.11,688.396 1782.09,691.094 1784.07,693.701 1786.05,696.221 1788.03,698.657 1790.01,701.01 1792,703.284 1793.98,705.481 1795.96,707.604 1797.94,709.654 \n",
       "  1799.92,711.635 1801.9,713.547 1803.89,715.395 1805.87,717.179 1807.85,718.902 1809.83,720.566 1811.81,722.173 1813.79,723.725 1815.78,725.223 1817.76,726.669 \n",
       "  1819.74,728.066 1821.72,729.414 1823.7,730.716 1825.68,731.973 1827.67,733.186 1829.65,734.357 1831.63,735.488 1833.61,736.579 1835.59,737.633 1837.57,738.65 \n",
       "  1839.56,739.631 1841.54,740.579 1843.52,741.494 1845.5,742.377 1847.48,743.229 1849.46,744.051 1851.45,744.845 1853.43,745.612 1855.41,746.352 1857.39,747.065 \n",
       "  1859.37,747.755 1861.35,748.42 1863.34,749.062 1865.32,749.681 1867.3,750.279 1869.28,750.857 1871.26,751.414 1873.25,751.952 1875.23,752.471 1877.21,752.972 \n",
       "  1879.19,753.455 1881.17,753.922 1883.15,754.372 1885.14,754.807 1887.12,755.226 1889.1,755.631 1891.08,756.022 1893.06,756.399 1895.04,756.763 1897.03,757.115 \n",
       "  1899.01,757.454 1900.99,757.781 1902.97,758.097 1904.95,758.402 1906.93,758.696 1908.92,758.98 1910.9,759.254 1912.88,759.519 1914.86,759.774 1916.84,760.021 \n",
       "  1918.82,760.259 1920.81,760.488 1922.79,760.71 1924.77,760.924 1926.75,761.13 1928.73,761.329 1930.71,761.522 1932.7,761.707 1934.68,761.886 1936.66,762.059 \n",
       "  1938.64,762.226 1940.62,762.387 1942.6,762.542 1944.59,762.692 1946.57,762.837 1948.55,762.977 1950.53,763.112 1952.51,763.242 1954.49,763.367 1956.48,763.489 \n",
       "  1958.46,763.606 1960.44,763.719 1962.42,763.828 1964.4,763.933 1966.38,764.034 1968.37,764.132 1970.35,764.227 1972.33,764.318 1974.31,764.406 1976.29,764.491 \n",
       "  1978.27,764.573 1980.26,764.653 1982.24,764.729 1984.22,764.803 1986.2,764.874 1988.18,764.943 1990.17,765.009 1992.15,765.073 1994.13,765.135 1996.11,765.194 \n",
       "  1998.09,765.252 2000.07,765.308 2002.06,765.361 2004.04,765.413 2006.02,765.463 2008,765.511 2009.98,765.558 2011.96,765.603 2013.95,765.646 2015.93,765.688 \n",
       "  2017.91,765.728 2019.89,765.767 2021.87,765.805 2023.85,765.841 2025.84,765.876 2027.82,765.91 2029.8,765.942 2031.78,765.974 2033.76,766.004 2035.74,766.034 \n",
       "  2037.73,766.062 2039.71,766.089 2041.69,766.116 2043.67,766.141 2045.65,766.166 2047.63,766.189 2049.62,766.212 2051.6,766.234 2053.58,766.256 2055.56,766.276 \n",
       "  2057.54,766.296 2059.52,766.315 2061.51,766.334 2063.49,766.352 2065.47,766.369 2067.45,766.386 2069.43,766.402 2071.41,766.417 2073.4,766.432 2075.38,766.447 \n",
       "  2077.36,766.46 2079.34,766.474 2081.32,766.487 2083.3,766.499 2085.29,766.511 2087.27,766.523 2089.25,766.534 2091.23,766.545 2093.21,766.556 2095.19,766.566 \n",
       "  2097.18,766.576 2099.16,766.585 2101.14,766.594 2103.12,766.603 2105.1,766.612 2107.09,766.62 2109.07,766.628 2111.05,766.635 2113.03,766.643 2115.01,766.65 \n",
       "  2116.99,766.657 2118.98,766.663 2120.96,766.67 2122.94,766.676 2124.92,766.682 2126.9,766.687 2128.88,766.693 2130.87,766.698 2132.85,766.704 2134.83,766.709 \n",
       "  2136.81,766.713 2138.79,766.718 2140.77,766.723 2142.76,766.727 2144.74,766.731 2146.72,766.735 2148.7,766.739 2150.68,766.743 2152.66,766.746 2154.65,766.75 \n",
       "  2156.63,766.753 2158.61,766.757 2160.59,766.76 2162.57,766.763 2164.55,766.766 2166.54,766.769 2168.52,766.771 2170.5,766.774 2172.48,766.777 2174.46,766.779 \n",
       "  2176.44,766.781 2178.43,766.784 2180.41,766.786 2182.39,766.788 2184.37,766.79 2186.35,766.792 2188.33,766.794 2190.32,766.796 2192.3,766.798 2194.28,766.8 \n",
       "  2196.26,766.801 2198.24,766.803 2200.22,766.805 2202.21,766.806 2204.19,766.808 2206.17,766.809 2208.15,766.811 2210.13,766.812 2212.12,766.813 2214.1,766.814 \n",
       "  2216.08,766.816 2218.06,766.817 2220.04,766.818 2222.02,766.819 2224.01,766.82 2225.99,766.821 2227.97,766.822 2229.95,766.823 2231.93,766.824 2233.91,766.825 \n",
       "  2235.9,766.826 2237.88,766.827 2239.86,766.828 2241.84,766.829 2243.82,766.829 2245.8,766.83 2247.79,766.831 2249.77,766.832 2251.75,766.833 2253.73,766.833 \n",
       "  2255.71,766.834 2257.69,766.835 2259.68,766.835 2261.66,766.836 2263.64,766.837 2265.62,766.837 2267.6,766.838 2269.58,766.839 2271.57,766.839 2273.55,766.84 \n",
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      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V0 = -5.0\n",
    "x0 = 3\n",
    "N = 1000\n",
    "xmax = 10.0\n",
    "xmin = -10.0\n",
    "xvec = range(xmin,xmax,length=N)\n",
    "mat_H2 = make_H1d(N,xmax,xmin,V2) \n",
    "energy2p,mat_v2 = eigen(mat_H2)\n",
    "println(\"ポテンシャル二つの時のエネルギー\")\n",
    "println(energy2p[1:10])\n",
    "println(\"ポテンシャル一つの時のエネルギー\")\n",
    "println(energy[1:10])\n",
    "using Plots\n",
    "plot(xvec,[mat_v2[:,1:2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "となる。この場合、縮退が解けて、波動関数が足し算された「結合性軌道」の方がエネルギーが低い。\n",
    "#### 1.1.3 周期的なポテンシャルの場合\n",
    "固体の状況に近づけるため、さらにポテンシャルを周期的に配置してみる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
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       "  835.831,228.987 837.912,237.941 839.993,247.31 842.073,257.106 844.154,267.337 846.235,278.012 848.316,289.138 850.397,300.724 852.478,312.775 854.559,325.299 \n",
       "  856.64,338.299 858.721,351.78 860.802,365.745 862.883,380.196 864.963,395.135 867.044,410.561 869.125,426.474 871.206,442.869 873.287,459.745 875.368,477.095 \n",
       "  877.449,494.912 879.53,513.19 881.611,531.918 883.692,551.084 885.773,570.678 887.854,590.684 889.934,611.086 892.015,631.867 894.096,653.009 896.177,674.489 \n",
       "  898.258,696.287 900.339,718.378 902.42,740.736 904.501,763.336 906.582,786.147 908.663,809.14 910.744,832.284 912.825,855.545 914.905,878.89 916.986,902.282 \n",
       "  919.067,925.686 921.148,949.064 923.229,972.376 925.31,995.584 927.391,1018.65 929.472,1041.52 931.553,1064.17 933.634,1086.55 935.715,1108.62 937.796,1130.33 \n",
       "  939.876,1151.64 941.957,1172.51 944.038,1192.9 946.119,1212.77 948.2,1232.07 950.281,1250.76 952.362,1268.8 954.443,1286.16 956.524,1302.8 958.605,1318.67 \n",
       "  960.686,1333.75 962.767,1347.99 964.847,1361.37 966.928,1373.86 969.009,1385.43 971.09,1396.04 973.171,1405.68 975.252,1414.33 977.333,1421.96 979.414,1428.55 \n",
       "  981.495,1434.09 983.576,1438.56 985.657,1441.97 987.738,1444.28 989.818,1445.51 991.899,1445.65 993.98,1444.69 996.061,1442.65 998.142,1439.52 1000.22,1435.31 \n",
       "  1002.3,1430.03 1004.38,1423.7 1006.47,1416.33 1008.55,1407.94 1010.63,1398.55 1012.71,1388.17 1014.79,1376.84 1016.87,1364.58 1018.95,1351.42 1021.03,1337.39 \n",
       "  1023.11,1322.51 1025.19,1306.84 1027.27,1290.39 1029.36,1273.21 1031.44,1255.33 1033.52,1236.8 1035.6,1217.65 1037.68,1197.92 1039.76,1177.66 1041.84,1156.9 \n",
       "  1043.92,1135.69 1046,1114.08 1048.08,1092.1 1050.17,1069.79 1052.25,1047.21 1054.33,1024.38 1056.41,1001.36 1058.49,978.189 1060.57,954.9 1062.65,931.535 \n",
       "  1064.73,908.134 1066.81,884.735 1068.89,861.375 1070.97,838.089 1073.06,814.913 1075.14,791.879 1077.22,769.02 1079.3,746.365 1081.38,723.943 1083.46,701.783 \n",
       "  1085.54,679.91 1087.62,658.348 1089.7,637.12 1091.78,616.246 1093.86,595.748 1095.95,575.641 1098.03,555.943 1100.11,536.669 1102.19,517.83 1104.27,499.439 \n",
       "  1106.35,481.505 1108.43,464.038 1110.51,447.043 1112.59,430.527 1114.67,414.494 1116.75,398.946 1118.84,383.885 1120.92,369.312 1123,355.225 1125.08,341.624 \n",
       "  1127.16,328.504 1129.24,315.862 1131.32,303.693 1133.4,291.991 1135.48,280.751 1137.56,269.964 1139.64,259.623 1141.73,249.719 1143.81,240.244 1145.89,231.187 \n",
       "  1147.97,222.539 1150.05,214.289 1152.13,206.428 1154.21,198.943 1156.29,191.824 1158.37,185.059 1160.45,178.638 1162.53,172.547 1164.62,166.777 1166.7,161.315 \n",
       "  1168.78,156.15 1170.86,151.271 1172.94,146.665 1175.02,142.323 1177.1,138.232 1179.18,134.382 1181.26,130.763 1183.34,127.364 1185.42,124.174 1187.51,121.184 \n",
       "  1189.59,118.384 1191.67,115.766 1193.75,113.319 1195.83,111.035 1197.91,108.905 1199.99,106.922 1202.07,105.078 1204.15,103.365 1206.23,101.777 1208.31,100.306 \n",
       "  1210.4,98.9454 1212.48,97.69 1214.56,96.5337 1216.64,95.4709 1218.72,94.4966 1220.8,93.606 1222.88,92.7946 1224.96,92.0582 1227.04,91.393 1229.12,90.7955 \n",
       "  1231.2,90.2625 1233.29,89.7909 1235.37,89.3783 1237.45,89.0223 1239.53,88.7209 1241.61,88.4723 1243.69,88.2752 1245.77,88.1283 1247.85,88.0309 1249.93,87.9823 \n",
       "  1252.01,87.9823 1254.09,88.0309 1256.18,88.1283 1258.26,88.2752 1260.34,88.4723 1262.42,88.7209 1264.5,89.0223 1266.58,89.3783 1268.66,89.7909 1270.74,90.2625 \n",
       "  1272.82,90.7955 1274.9,91.393 1276.98,92.0582 1279.07,92.7946 1281.15,93.606 1283.23,94.4966 1285.31,95.4709 1287.39,96.5337 1289.47,97.69 1291.55,98.9454 \n",
       "  1293.63,100.306 1295.71,101.777 1297.79,103.365 1299.87,105.078 1301.96,106.922 1304.04,108.905 1306.12,111.035 1308.2,113.319 1310.28,115.766 1312.36,118.384 \n",
       "  1314.44,121.184 1316.52,124.174 1318.6,127.364 1320.68,130.763 1322.76,134.382 1324.85,138.232 1326.93,142.323 1329.01,146.665 1331.09,151.271 1333.17,156.15 \n",
       "  1335.25,161.315 1337.33,166.777 1339.41,172.547 1341.49,178.638 1343.57,185.059 1345.66,191.824 1347.74,198.943 1349.82,206.428 1351.9,214.289 1353.98,222.539 \n",
       "  1356.06,231.187 1358.14,240.244 1360.22,249.719 1362.3,259.623 1364.38,269.964 1366.46,280.751 1368.55,291.991 1370.63,303.693 1372.71,315.862 1374.79,328.504 \n",
       "  1376.87,341.624 1378.95,355.225 1381.03,369.312 1383.11,383.885 1385.19,398.946 1387.27,414.494 1389.35,430.527 1391.44,447.043 1393.52,464.038 1395.6,481.505 \n",
       "  1397.68,499.439 1399.76,517.83 1401.84,536.669 1403.92,555.943 1406,575.641 1408.08,595.748 1410.16,616.246 1412.24,637.12 1414.33,658.348 1416.41,679.91 \n",
       "  1418.49,701.783 1420.57,723.943 1422.65,746.365 1424.73,769.02 1426.81,791.879 1428.89,814.913 1430.97,838.089 1433.05,861.375 1435.13,884.735 1437.22,908.134 \n",
       "  1439.3,931.535 1441.38,954.9 1443.46,978.189 1445.54,1001.36 1447.62,1024.38 1449.7,1047.21 1451.78,1069.79 1453.86,1092.1 1455.94,1114.08 1458.02,1135.69 \n",
       "  1460.11,1156.9 1462.19,1177.66 1464.27,1197.92 1466.35,1217.65 1468.43,1236.8 1470.51,1255.33 1472.59,1273.21 1474.67,1290.39 1476.75,1306.84 1478.83,1322.51 \n",
       "  1480.91,1337.39 1483,1351.42 1485.08,1364.58 1487.16,1376.84 1489.24,1388.17 1491.32,1398.55 1493.4,1407.94 1495.48,1416.33 1497.56,1423.7 1499.64,1430.03 \n",
       "  1501.72,1435.31 1503.8,1439.52 1505.89,1442.65 1507.97,1444.69 1510.05,1445.65 1512.13,1445.51 1514.21,1444.28 1516.29,1441.97 1518.37,1438.56 1520.45,1434.09 \n",
       "  1522.53,1428.55 1524.61,1421.96 1526.69,1414.33 1528.78,1405.68 1530.86,1396.04 1532.94,1385.43 1535.02,1373.86 1537.1,1361.37 1539.18,1347.99 1541.26,1333.75 \n",
       "  1543.34,1318.67 1545.42,1302.8 1547.5,1286.16 1549.58,1268.8 1551.67,1250.76 1553.75,1232.07 1555.83,1212.77 1557.91,1192.9 1559.99,1172.51 1562.07,1151.64 \n",
       "  1564.15,1130.33 1566.23,1108.62 1568.31,1086.55 1570.39,1064.17 1572.47,1041.52 1574.56,1018.65 1576.64,995.584 1578.72,972.376 1580.8,949.064 1582.88,925.686 \n",
       "  1584.96,902.282 1587.04,878.89 1589.12,855.545 1591.2,832.284 1593.28,809.14 1595.36,786.147 1597.45,763.336 1599.53,740.736 1601.61,718.378 1603.69,696.287 \n",
       "  1605.77,674.489 1607.85,653.009 1609.93,631.867 1612.01,611.086 1614.09,590.684 1616.17,570.678 1618.26,551.084 1620.34,531.918 1622.42,513.19 1624.5,494.912 \n",
       "  1626.58,477.095 1628.66,459.745 1630.74,442.869 1632.82,426.474 1634.9,410.561 1636.98,395.135 1639.06,380.196 1641.15,365.745 1643.23,351.78 1645.31,338.299 \n",
       "  1647.39,325.299 1649.47,312.775 1651.55,300.724 1653.63,289.138 1655.71,278.012 1657.79,267.337 1659.87,257.106 1661.95,247.31 1664.04,237.941 1666.12,228.987 \n",
       "  1668.2,220.44 1670.28,212.288 1672.36,204.522 1674.44,197.129 1676.52,190.1 1678.6,183.422 1680.68,177.084 1682.76,171.075 1684.84,165.383 1686.93,159.997 \n",
       "  1689.01,154.904 1691.09,150.094 1693.17,145.556 1695.25,141.277 1697.33,137.248 1699.41,133.456 1701.49,129.893 1703.57,126.547 1705.65,123.408 1707.73,120.467 \n",
       "  1709.82,117.713 1711.9,115.138 1713.98,112.733 1716.06,110.488 1718.14,108.396 1720.22,106.449 1722.3,104.638 1724.38,102.957 1726.46,101.398 1728.54,99.9555 \n",
       "  1730.62,98.622 1732.71,97.3919 1734.79,96.2594 1736.87,95.2192 1738.95,94.2663 1741.03,93.3959 1743.11,92.6036 1745.19,91.8854 1747.27,91.2375 1749.35,90.6563 \n",
       "  1751.43,90.1389 1753.51,89.6824 1755.6,89.2841 1757.68,88.9419 1759.76,88.6539 1761.84,88.4183 1763.92,88.2338 1766,88.0994 1768.08,88.0142 1770.16,87.9778 \n",
       "  1772.24,87.9899 1774.32,88.0507 1776.4,88.1604 1778.49,88.3197 1780.57,88.5296 1782.65,88.7912 1784.73,89.1061 1786.81,89.4761 1788.89,89.9032 1790.97,90.3899 \n",
       "  1793.05,90.9387 1795.13,91.5529 1797.21,92.2355 1799.29,92.9903 1801.38,93.8211 1803.46,94.7322 1805.54,95.7281 1807.62,96.8138 1809.7,97.9944 1811.78,99.2754 \n",
       "  1813.86,100.663 1815.94,102.163 1818.02,103.782 1820.1,105.527 1822.18,107.405 1824.27,109.423 1826.35,111.591 1828.43,113.915 1830.51,116.404 1832.59,119.067 \n",
       "  1834.67,121.913 1836.75,124.952 1838.83,128.193 1840.91,131.647 1842.99,135.323 1845.07,139.232 1847.16,143.384 1849.24,147.792 1851.32,152.465 1853.4,157.414 \n",
       "  1855.48,162.653 1857.56,168.19 1859.64,174.04 1861.72,180.212 1863.8,186.718 1865.88,193.57 1867.96,200.779 1870.05,208.357 1872.13,216.315 1874.21,224.663 \n",
       "  1876.29,233.412 1878.37,242.573 1880.45,252.154 1882.53,262.167 1884.61,272.618 1886.69,283.518 1888.77,294.873 1890.86,306.691 1892.94,318.978 1895.02,331.739 \n",
       "  1897.1,344.979 1899.18,358.702 1901.26,372.91 1903.34,387.605 1905.42,402.787 1907.5,418.457 1909.58,434.611 1911.66,451.247 1913.75,468.361 1915.83,485.945 \n",
       "  1917.91,503.994 1919.99,522.498 1922.07,541.447 1924.15,560.829 1926.23,580.63 1928.31,600.836 1930.39,621.43 1932.47,642.394 1934.55,663.708 1936.64,685.35 \n",
       "  1938.72,707.297 1940.8,729.525 1942.88,752.008 1944.96,774.716 1947.04,797.623 1949.12,820.695 1951.2,843.902 1953.28,867.209 1955.36,890.582 1957.44,913.985 \n",
       "  1959.53,937.381 1961.61,960.731 1963.69,983.996 1965.77,1007.14 1967.85,1030.11 1969.93,1052.88 1972.01,1075.4 1974.09,1097.62 1976.17,1119.52 1978.25,1141.03 \n",
       "  1980.33,1162.13 1982.42,1182.77 1984.5,1202.9 1986.58,1222.49 1988.66,1241.49 1990.74,1259.86 1992.82,1277.57 1994.9,1294.57 1996.98,1310.83 1999.06,1326.31 \n",
       "  2001.14,1340.97 2003.22,1354.79 2005.31,1367.73 2007.39,1379.76 2009.47,1390.86 2011.55,1400.99 2013.63,1410.13 2015.71,1418.27 2017.79,1425.38 2019.87,1431.45 \n",
       "  2021.95,1436.46 2024.03,1440.4 2026.11,1443.26 2028.2,1445.03 2030.28,1445.72 2032.36,1445.31 2034.44,1443.81 2036.52,1441.22 2038.6,1437.55 2040.68,1432.8 \n",
       "  2042.76,1427 2044.84,1420.15 2046.92,1412.26 2049,1403.37 2051.09,1393.48 2053.17,1382.62 2055.25,1370.82 2057.33,1358.11 2059.41,1344.51 2061.49,1330.05 \n",
       "  2063.57,1314.77 2065.65,1298.71 2067.73,1281.89 2069.81,1264.35 2071.89,1246.14 2073.98,1227.3 2076.06,1207.85 2078.14,1187.85 2080.22,1167.34 2082.3,1146.35 \n",
       "  2084.38,1124.93 2086.46,1103.13 2088.54,1080.98 2090.62,1058.53 2092.7,1035.82 2094.78,1012.9 2096.87,989.794 2098.95,966.556 2101.03,943.224 2103.11,919.836 \n",
       "  2105.19,896.432 2107.27,873.048 2109.35,849.72 2111.43,826.485 2113.51,803.376 2115.59,780.426 2117.67,757.665 2119.76,735.123 2121.84,712.829 2123.92,690.809 \n",
       "  2126,669.088 2128.08,647.691 2130.16,626.637 2132.24,605.949 2134.32,585.644 2136.4,565.74 2138.48,546.252 2140.56,527.194 2142.65,508.578 2144.73,490.414 \n",
       "  2146.81,472.713 2148.89,455.481 2150.97,438.725 2153.05,422.45 2155.13,406.659 2157.21,391.355 2159.29,376.538 2161.37,362.208 2163.45,348.364 2165.54,335.004 \n",
       "  2167.62,322.123 2169.7,309.719 2171.78,297.784 2173.86,286.314 2175.94,275.301 2178.02,264.738 2180.1,254.617 2182.18,244.928 2184.26,235.664 2186.35,226.812 \n",
       "  2188.43,218.365 2190.51,210.311 2192.59,202.639 2194.67,195.338 2196.75,188.398 2198.83,181.806 2200.91,175.552 2202.99,169.623 2205.07,164.009 2207.15,158.697 \n",
       "  2209.24,153.676 2211.32,148.935 2213.4,144.462 2215.48,140.247 2217.56,136.278 2219.64,132.545 2221.72,129.037 2223.8,125.743 2225.88,122.655 2227.96,119.761 \n",
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      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function Vp(x,V0,xmax,xmin,np)\n",
    "    dx = (xmax-xmin)/(np-1)\n",
    "    V3 = 0.0\n",
    "    for i=1:np-1\n",
    "        x0 = (i-1)*dx + xmin+dx/2\n",
    "        V3 += V0*exp(-(x-x0)^2)+V0*exp(-(x-(xmax-xmin)-x0)^2)+V0*exp(-(x+(xmax-xmin)-x0)^2)\n",
    "    end\n",
    "    return V3\n",
    "end\n",
    "\n",
    "N = 2000\n",
    "xmax = 10.0\n",
    "xmin = -10.0\n",
    "\n",
    "V3(x) =  Vp(x,V0,xmax,xmin,5)\n",
    "plot(xvec,V3.(xvec),label=\"Potential\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "そして、ハミルトニアンに周期境界条件を課す。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "make_H1dp (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function make_H1dp(N,xmax,xmin,V)\n",
    "    mat_H = zeros(Float64,N,N)\n",
    "    a = (xmax-xmin)/(N-1)\n",
    "        \n",
    "    for i in 1:N\n",
    "        x = (i-1)*a + xmin\n",
    "        for dx in -1:1\n",
    "            j = i + dx\n",
    "            j += ifelse(j > N,-N,0)\n",
    "            j+= ifelse(j <1,+N,0)\n",
    "            \n",
    "            v = 0.0\n",
    "            if dx == 0                \n",
    "                v = (2/a^2 + V(x))\n",
    "            elseif dx == 1\n",
    "                v = -1/a^2\n",
    "            elseif dx == -1\n",
    "                v = -1/a^2\n",
    "            end\n",
    "            \n",
    "            if 1 <= j <= N\n",
    "                mat_H[i,j] = v\n",
    "            end\n",
    "            \n",
    "        end\n",
    "        \n",
    "    end\n",
    "    \n",
    "    return mat_H\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "周期ポテンシャルの時のエネルギー\n",
      "[-3.1464447984917503, -3.1404344051833117, -3.1403806125861387, -3.1342700928874323, -0.5439642693009712, -0.3966847995080151, -0.39613473223049867, -0.14398863565515585, 0.4934084688978966, 1.0192066655092875]\n",
      "ポテンシャル一つの時のエネルギー\n",
      "[-3.1404009040145286, -0.4062142205546486, 0.10339356506001751, 0.15632796480264988, 0.4145932097452478, 0.5822287366538306, 0.9363743175283377, 1.2355092013437883, 1.6711811288154879, 2.0989689480359477]\n"
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       "  656.427,986.332 657.432,982.969 658.436,979.649 659.44,976.372 660.445,973.138 661.449,969.947 662.453,966.799 663.458,963.693 664.462,960.63 665.467,957.609 \n",
       "  666.471,954.63 667.475,951.693 668.48,948.797 669.484,945.944 670.488,943.131 671.493,940.359 672.497,937.628 673.501,934.938 674.506,932.287 675.51,929.676 \n",
       "  676.514,927.105 677.519,924.573 678.523,922.08 679.528,919.626 680.532,917.21 681.536,914.832 682.541,912.491 683.545,910.188 684.549,907.922 685.554,905.692 \n",
       "  686.558,903.499 687.562,901.341 688.567,899.219 689.571,897.132 690.575,895.08 691.58,893.062 692.584,891.079 693.589,889.129 694.593,887.212 695.597,885.329 \n",
       "  696.602,883.478 697.606,881.659 698.61,879.872 699.615,878.117 700.619,876.393 701.623,874.699 702.628,873.036 703.632,871.403 704.636,869.8 705.641,868.227 \n",
       "  706.645,866.682 707.65,865.166 708.654,863.678 709.658,862.219 710.663,860.787 711.667,859.382 712.671,858.004 713.676,856.653 714.68,855.329 715.684,854.03 \n",
       "  716.689,852.757 717.693,851.51 718.697,850.287 719.702,849.09 720.706,847.916 721.71,846.767 722.715,845.642 723.719,844.54 724.724,843.462 725.728,842.407 \n",
       "  726.732,841.374 727.737,840.364 728.741,839.376 729.745,838.41 730.75,837.466 731.754,836.543 732.758,835.642 733.763,834.761 734.767,833.901 735.771,833.061 \n",
       "  736.776,832.242 737.78,831.443 738.785,830.663 739.789,829.903 740.793,829.162 741.798,828.441 742.802,827.738 743.806,827.055 744.811,826.389 745.815,825.742 \n",
       "  746.819,825.114 747.824,824.503 748.828,823.91 749.832,823.335 750.837,822.777 751.841,822.236 752.846,821.713 753.85,821.207 754.854,820.717 755.859,820.244 \n",
       "  756.863,819.788 757.867,819.349 758.872,818.925 759.876,818.518 760.88,818.127 761.885,817.752 762.889,817.393 763.893,817.049 764.898,816.722 765.902,816.409 \n",
       "  766.907,816.113 767.911,815.831 768.915,815.565 769.92,815.314 770.924,815.078 771.928,814.858 772.933,814.652 773.937,814.461 774.941,814.285 775.946,814.124 \n",
       "  776.95,813.978 777.954,813.847 778.959,813.73 779.963,813.628 780.968,813.54 781.972,813.467 782.976,813.409 783.981,813.365 784.985,813.336 785.989,813.322 \n",
       "  786.994,813.322 787.998,813.336 789.002,813.365 790.007,813.409 791.011,813.467 792.015,813.54 793.02,813.627 794.024,813.729 795.029,813.846 796.033,813.978 \n",
       "  797.037,814.124 798.042,814.285 799.046,814.46 800.05,814.651 801.055,814.857 802.059,815.077 803.063,815.313 804.068,815.564 805.072,815.83 806.076,816.111 \n",
       "  807.081,816.408 808.085,816.72 809.09,817.048 810.094,817.392 811.098,817.751 812.103,818.126 813.107,818.517 814.111,818.924 815.116,819.347 816.12,819.787 \n",
       "  817.124,820.243 818.129,820.716 819.133,821.205 820.137,821.711 821.142,822.235 822.146,822.775 823.151,823.333 824.155,823.908 825.159,824.501 826.164,825.112 \n",
       "  827.168,825.741 828.172,826.388 829.177,827.053 830.181,827.737 831.185,828.44 832.19,829.161 833.194,829.902 834.198,830.662 835.203,831.442 836.207,832.241 \n",
       "  837.212,833.061 838.216,833.9 839.22,834.761 840.225,835.642 841.229,836.543 842.233,837.466 843.238,838.411 844.242,839.377 845.246,840.365 846.251,841.375 \n",
       "  847.255,842.408 848.259,843.464 849.264,844.542 850.268,845.644 851.273,846.77 852.277,847.919 853.281,849.093 854.286,850.291 855.29,851.514 856.294,852.762 \n",
       "  857.299,854.036 858.303,855.335 859.307,856.66 860.312,858.012 861.316,859.39 862.32,860.795 863.325,862.228 864.329,863.689 865.334,865.177 866.338,866.694 \n",
       "  867.342,868.24 868.347,869.814 869.351,871.418 870.355,873.052 871.36,874.716 872.364,876.411 873.368,878.136 874.373,879.893 875.377,881.681 876.381,883.502 \n",
       "  877.386,885.354 878.39,887.24 879.395,889.158 880.399,891.11 881.403,893.095 882.408,895.115 883.412,897.169 884.416,899.258 885.421,901.383 886.425,903.543 \n",
       "  887.429,905.739 888.434,907.971 889.438,910.24 890.442,912.547 891.447,914.89 892.451,917.272 893.456,919.691 894.46,922.149 895.464,924.646 896.469,927.181 \n",
       "  897.473,929.757 898.477,932.371 899.482,935.026 900.486,937.722 901.49,940.458 902.495,943.234 903.499,946.052 904.503,948.912 905.508,951.813 906.512,954.756 \n",
       "  907.517,957.741 908.521,960.768 909.525,963.838 910.53,966.951 911.534,970.107 912.538,973.305 913.543,976.547 914.547,979.832 915.551,983.161 916.556,986.533 \n",
       "  917.56,989.949 918.564,993.408 919.569,996.911 920.573,1000.46 921.578,1004.05 922.582,1007.68 923.586,1011.36 924.591,1015.08 925.595,1018.84 926.599,1022.65 \n",
       "  927.604,1026.5 928.608,1030.39 929.612,1034.33 930.617,1038.31 931.621,1042.33 932.625,1046.39 933.63,1050.49 934.634,1054.63 935.639,1058.82 936.643,1063.04 \n",
       "  937.647,1067.3 938.652,1071.61 939.656,1075.95 940.66,1080.32 941.665,1084.74 942.669,1089.19 943.673,1093.68 944.678,1098.2 945.682,1102.76 946.686,1107.35 \n",
       "  947.691,1111.97 948.695,1116.62 949.7,1121.31 950.704,1126.02 951.708,1130.76 952.713,1135.53 953.717,1140.33 954.721,1145.15 955.726,1149.99 956.73,1154.86 \n",
       "  957.734,1159.74 958.739,1164.65 959.743,1169.57 960.747,1174.51 961.752,1179.47 962.756,1184.44 963.76,1189.42 964.765,1194.41 965.769,1199.41 966.774,1204.41 \n",
       "  967.778,1209.42 968.782,1214.44 969.787,1219.45 970.791,1224.47 971.795,1229.48 972.8,1234.49 973.804,1239.49 974.808,1244.48 975.813,1249.46 976.817,1254.43 \n",
       "  977.821,1259.38 978.826,1264.31 979.83,1269.23 980.835,1274.12 981.839,1278.99 982.843,1283.83 983.848,1288.64 984.852,1293.42 985.856,1298.17 986.861,1302.88 \n",
       "  987.865,1307.55 988.869,1312.18 989.874,1316.77 990.878,1321.31 991.882,1325.8 992.887,1330.24 993.891,1334.63 994.896,1338.96 995.9,1343.23 996.904,1347.44 \n",
       "  997.909,1351.59 998.913,1355.67 999.917,1359.69 1000.92,1363.63 1001.93,1367.5 1002.93,1371.29 1003.93,1375.01 1004.94,1378.65 1005.94,1382.2 1006.95,1385.67 \n",
       "  1007.95,1389.05 1008.96,1392.34 1009.96,1395.54 1010.97,1398.65 1011.97,1401.66 1012.97,1404.58 1013.98,1407.39 1014.98,1410.11 1015.99,1412.72 1016.99,1415.22 \n",
       "  1018,1417.62 1019,1419.91 1020,1422.09 1021.01,1424.16 1022.01,1426.11 1023.02,1427.95 1024.02,1429.68 1025.03,1431.29 1026.03,1432.78 1027.03,1434.15 \n",
       "  1028.04,1435.4 1029.04,1436.53 1030.05,1437.54 1031.05,1438.43 1032.06,1439.19 1033.06,1439.83 1034.07,1440.34 1035.07,1440.74 1036.07,1441 1037.08,1441.14 \n",
       "  1038.08,1441.16 1039.09,1441.05 1040.09,1440.81 1041.1,1440.45 1042.1,1439.97 1043.1,1439.36 1044.11,1438.63 1045.11,1437.78 1046.12,1436.8 1047.12,1435.7 \n",
       "  1048.13,1434.48 1049.13,1433.14 1050.14,1431.68 1051.14,1430.1 1052.14,1428.4 1053.15,1426.59 1054.15,1424.66 1055.16,1422.62 1056.16,1420.47 1057.17,1418.21 \n",
       "  1058.17,1415.84 1059.17,1413.36 1060.18,1410.77 1061.18,1408.09 1062.19,1405.3 1063.19,1402.41 1064.2,1399.42 1065.2,1396.34 1066.2,1393.16 1067.21,1389.89 \n",
       "  1068.21,1386.53 1069.22,1383.08 1070.22,1379.55 1071.23,1375.94 1072.23,1372.24 1073.24,1368.46 1074.24,1364.61 1075.24,1360.69 1076.25,1356.69 1077.25,1352.63 \n",
       "  1078.26,1348.49 1079.26,1344.3 1080.27,1340.04 1081.27,1335.73 1082.27,1331.35 1083.28,1326.92 1084.28,1322.44 1085.29,1317.92 1086.29,1313.34 1087.3,1308.72 \n",
       "  1088.3,1304.06 1089.31,1299.36 1090.31,1294.62 1091.31,1289.85 1092.32,1285.05 1093.32,1280.21 1094.33,1275.35 1095.33,1270.46 1096.34,1265.56 1097.34,1260.63 \n",
       "  1098.34,1255.68 1099.35,1250.72 1100.35,1245.74 1101.36,1240.75 1102.36,1235.75 1103.37,1230.75 1104.37,1225.74 1105.37,1220.72 1106.38,1215.71 1107.38,1210.69 \n",
       "  1108.39,1205.68 1109.39,1200.67 1110.4,1195.67 1111.4,1190.68 1112.41,1185.7 1113.41,1180.73 1114.41,1175.77 1115.42,1170.82 1116.42,1165.89 1117.43,1160.98 \n",
       "  1118.43,1156.09 1119.44,1151.22 1120.44,1146.37 1121.44,1141.55 1122.45,1136.75 1123.45,1131.97 1124.46,1127.22 1125.46,1122.5 1126.47,1117.81 1127.47,1113.15 \n",
       "  1128.48,1108.52 1129.48,1103.92 1130.48,1099.36 1131.49,1094.83 1132.49,1090.33 1133.5,1085.87 1134.5,1081.45 1135.51,1077.06 1136.51,1072.71 1137.51,1068.4 \n",
       "  1138.52,1064.12 1139.52,1059.89 1140.53,1055.7 1141.53,1051.54 1142.54,1047.43 1143.54,1043.36 1144.54,1039.33 1145.55,1035.34 1146.55,1031.4 1147.56,1027.49 \n",
       "  1148.56,1023.63 1149.57,1019.82 1150.57,1016.04 1151.58,1012.31 1152.58,1008.62 1153.58,1004.98 1154.59,1001.38 1155.59,997.821 1156.6,994.307 1157.6,990.837 \n",
       "  1158.61,987.411 1159.61,984.028 1160.61,980.689 1161.62,977.393 1162.62,974.141 1163.63,970.932 1164.63,967.766 1165.64,964.643 1166.64,961.563 1167.64,958.525 \n",
       "  1168.65,955.53 1169.65,952.576 1170.66,949.665 1171.66,946.796 1172.67,943.968 1173.67,941.182 1174.68,938.436 1175.68,935.731 1176.68,933.066 1177.69,930.442 \n",
       "  1178.69,927.857 1179.7,925.312 1180.7,922.806 1181.71,920.339 1182.71,917.911 1183.71,915.52 1184.72,913.168 1185.72,910.853 1186.73,908.575 1187.73,906.334 \n",
       "  1188.74,904.13 1189.74,901.961 1190.75,899.828 1191.75,897.731 1192.75,895.669 1193.76,893.641 1194.76,891.648 1195.77,889.688 1196.77,887.762 1197.78,885.869 \n",
       "  1198.78,884.009 1199.78,882.182 1200.79,880.386 1201.79,878.622 1202.8,876.89 1203.8,875.188 1204.81,873.517 1205.81,871.877 1206.81,870.266 1207.82,868.685 \n",
       "  1208.82,867.133 1209.83,865.61 1210.83,864.115 1211.84,862.648 1212.84,861.21 1213.85,859.798 1214.85,858.414 1215.85,857.057 1216.86,855.726 1217.86,854.421 \n",
       "  1218.87,853.142 1219.87,851.889 1220.88,850.661 1221.88,849.458 1222.88,848.279 1223.89,847.125 1224.89,845.994 1225.9,844.888 1226.9,843.804 1227.91,842.744 \n",
       "  1228.91,841.707 1229.92,840.692 1230.92,839.7 1231.92,838.729 1232.93,837.781 1233.93,836.854 1234.94,835.948 1235.94,835.063 1236.95,834.199 1237.95,833.356 \n",
       "  1238.95,832.533 1239.96,831.73 1240.96,830.947 1241.97,830.183 1242.97,829.439 1243.98,828.715 1244.98,828.009 1245.98,827.322 1246.99,826.654 1247.99,826.004 \n",
       "  1249,825.372 1250,824.759 1251.01,824.163 1252.01,823.585 1253.02,823.025 1254.02,822.482 1255.02,821.956 1256.03,821.448 1257.03,820.956 1258.04,820.482 \n",
       "  1259.04,820.023 1260.05,819.582 1261.05,819.157 1262.05,818.748 1263.06,818.355 1264.06,817.978 1265.07,817.617 1266.07,817.272 1267.08,816.943 1268.08,816.629 \n",
       "  1269.08,816.331 1270.09,816.049 1271.09,815.781 1272.1,815.53 1273.1,815.293 1274.11,815.071 1275.11,814.865 1276.12,814.673 1277.12,814.496 1278.12,814.335 \n",
       "  1279.13,814.188 1280.13,814.056 1281.14,813.938 1282.14,813.836 1283.15,813.748 1284.15,813.675 1285.15,813.616 1286.16,813.573 1287.16,813.543 1288.17,813.529 \n",
       "  1289.17,813.529 1290.18,813.543 1291.18,813.573 1292.19,813.616 1293.19,813.675 1294.19,813.748 1295.2,813.836 1296.2,813.938 1297.21,814.056 1298.21,814.188 \n",
       "  1299.22,814.335 1300.22,814.496 1301.22,814.673 1302.23,814.865 1303.23,815.071 1304.24,815.293 1305.24,815.53 1306.25,815.781 1307.25,816.049 1308.25,816.331 \n",
       "  1309.26,816.629 1310.26,816.943 1311.27,817.272 1312.27,817.617 1313.28,817.978 1314.28,818.355 1315.29,818.748 1316.29,819.157 1317.29,819.582 1318.3,820.023 \n",
       "  1319.3,820.482 1320.31,820.956 1321.31,821.448 1322.32,821.956 1323.32,822.482 1324.32,823.025 1325.33,823.585 1326.33,824.163 1327.34,824.759 1328.34,825.372 \n",
       "  1329.35,826.004 1330.35,826.654 1331.36,827.322 1332.36,828.009 1333.36,828.715 1334.37,829.439 1335.37,830.183 1336.38,830.947 1337.38,831.73 1338.39,832.533 \n",
       "  1339.39,833.356 1340.39,834.199 1341.4,835.063 1342.4,835.948 1343.41,836.854 1344.41,837.781 1345.42,838.729 1346.42,839.7 1347.42,840.692 1348.43,841.707 \n",
       "  1349.43,842.744 1350.44,843.804 1351.44,844.888 1352.45,845.994 1353.45,847.125 1354.46,848.279 1355.46,849.458 1356.46,850.661 1357.47,851.889 1358.47,853.142 \n",
       "  1359.48,854.421 1360.48,855.726 1361.49,857.057 1362.49,858.414 1363.49,859.798 1364.5,861.21 1365.5,862.648 1366.51,864.115 1367.51,865.61 1368.52,867.133 \n",
       "  1369.52,868.685 1370.53,870.266 1371.53,871.877 1372.53,873.517 1373.54,875.188 1374.54,876.89 1375.55,878.622 1376.55,880.386 1377.56,882.182 1378.56,884.009 \n",
       "  1379.56,885.869 1380.57,887.762 1381.57,889.688 1382.58,891.648 1383.58,893.641 1384.59,895.669 1385.59,897.731 1386.59,899.828 1387.6,901.961 1388.6,904.13 \n",
       "  1389.61,906.334 1390.61,908.575 1391.62,910.853 1392.62,913.168 1393.63,915.52 1394.63,917.911 1395.63,920.339 1396.64,922.806 1397.64,925.312 1398.65,927.857 \n",
       "  1399.65,930.442 1400.66,933.066 1401.66,935.731 1402.66,938.436 1403.67,941.182 1404.67,943.968 1405.68,946.796 1406.68,949.665 1407.69,952.576 1408.69,955.53 \n",
       "  1409.69,958.525 1410.7,961.563 1411.7,964.643 1412.71,967.766 1413.71,970.932 1414.72,974.141 1415.72,977.393 1416.73,980.689 1417.73,984.028 1418.73,987.411 \n",
       "  1419.74,990.837 1420.74,994.307 1421.75,997.821 1422.75,1001.38 1423.76,1004.98 1424.76,1008.62 1425.76,1012.31 1426.77,1016.04 1427.77,1019.82 1428.78,1023.63 \n",
       "  1429.78,1027.49 1430.79,1031.4 1431.79,1035.34 1432.8,1039.33 1433.8,1043.36 1434.8,1047.43 1435.81,1051.54 1436.81,1055.7 1437.82,1059.89 1438.82,1064.12 \n",
       "  1439.83,1068.4 1440.83,1072.71 1441.83,1077.06 1442.84,1081.45 1443.84,1085.87 1444.85,1090.33 1445.85,1094.83 1446.86,1099.36 1447.86,1103.92 1448.86,1108.52 \n",
       "  1449.87,1113.15 1450.87,1117.81 1451.88,1122.5 1452.88,1127.22 1453.89,1131.97 1454.89,1136.75 1455.9,1141.55 1456.9,1146.37 1457.9,1151.22 1458.91,1156.09 \n",
       "  1459.91,1160.98 1460.92,1165.89 1461.92,1170.82 1462.93,1175.77 1463.93,1180.73 1464.93,1185.7 1465.94,1190.68 1466.94,1195.67 1467.95,1200.67 1468.95,1205.68 \n",
       "  1469.96,1210.69 1470.96,1215.71 1471.97,1220.72 1472.97,1225.74 1473.97,1230.75 1474.98,1235.75 1475.98,1240.75 1476.99,1245.74 1477.99,1250.72 1479,1255.68 \n",
       "  1480,1260.63 1481,1265.56 1482.01,1270.46 1483.01,1275.35 1484.02,1280.21 1485.02,1285.05 1486.03,1289.85 1487.03,1294.62 1488.03,1299.36 1489.04,1304.06 \n",
       "  1490.04,1308.72 1491.05,1313.34 1492.05,1317.92 1493.06,1322.44 1494.06,1326.92 1495.07,1331.35 1496.07,1335.73 1497.07,1340.04 1498.08,1344.3 1499.08,1348.49 \n",
       "  1500.09,1352.63 1501.09,1356.69 1502.1,1360.69 1503.1,1364.61 1504.1,1368.46 1505.11,1372.24 1506.11,1375.94 1507.12,1379.55 1508.12,1383.08 1509.13,1386.53 \n",
       "  1510.13,1389.89 1511.13,1393.16 1512.14,1396.34 1513.14,1399.42 1514.15,1402.41 1515.15,1405.3 1516.16,1408.09 1517.16,1410.77 1518.17,1413.36 1519.17,1415.84 \n",
       "  1520.17,1418.21 1521.18,1420.47 1522.18,1422.62 1523.19,1424.66 1524.19,1426.59 1525.2,1428.4 1526.2,1430.1 1527.2,1431.68 1528.21,1433.14 1529.21,1434.48 \n",
       "  1530.22,1435.7 1531.22,1436.8 1532.23,1437.78 1533.23,1438.63 1534.24,1439.36 1535.24,1439.97 1536.24,1440.45 1537.25,1440.81 1538.25,1441.05 1539.26,1441.16 \n",
       "  1540.26,1441.14 1541.27,1441 1542.27,1440.74 1543.27,1440.34 1544.28,1439.83 1545.28,1439.19 1546.29,1438.43 1547.29,1437.54 1548.3,1436.53 1549.3,1435.4 \n",
       "  1550.3,1434.15 1551.31,1432.78 1552.31,1431.29 1553.32,1429.68 1554.32,1427.95 1555.33,1426.11 1556.33,1424.16 1557.34,1422.09 1558.34,1419.91 1559.34,1417.62 \n",
       "  1560.35,1415.22 1561.35,1412.72 1562.36,1410.11 1563.36,1407.39 1564.37,1404.58 1565.37,1401.66 1566.37,1398.65 1567.38,1395.54 1568.38,1392.34 1569.39,1389.05 \n",
       "  1570.39,1385.67 1571.4,1382.2 1572.4,1378.65 1573.41,1375.01 1574.41,1371.29 1575.41,1367.5 1576.42,1363.63 1577.42,1359.69 1578.43,1355.67 1579.43,1351.59 \n",
       "  1580.44,1347.44 1581.44,1343.23 1582.44,1338.96 1583.45,1334.63 1584.45,1330.24 1585.46,1325.8 1586.46,1321.31 1587.47,1316.77 1588.47,1312.18 1589.47,1307.55 \n",
       "  1590.48,1302.88 1591.48,1298.17 1592.49,1293.42 1593.49,1288.64 1594.5,1283.83 1595.5,1278.99 1596.51,1274.12 1597.51,1269.23 1598.51,1264.31 1599.52,1259.38 \n",
       "  1600.52,1254.43 1601.53,1249.46 1602.53,1244.48 1603.54,1239.49 1604.54,1234.49 1605.54,1229.48 1606.55,1224.47 1607.55,1219.45 1608.56,1214.44 1609.56,1209.42 \n",
       "  1610.57,1204.41 1611.57,1199.41 1612.58,1194.41 1613.58,1189.42 1614.58,1184.44 1615.59,1179.47 1616.59,1174.51 1617.6,1169.57 1618.6,1164.65 1619.61,1159.74 \n",
       "  1620.61,1154.86 1621.61,1149.99 1622.62,1145.15 1623.62,1140.33 1624.63,1135.53 1625.63,1130.76 1626.64,1126.02 1627.64,1121.31 1628.64,1116.62 1629.65,1111.97 \n",
       "  1630.65,1107.35 1631.66,1102.76 1632.66,1098.2 1633.67,1093.68 1634.67,1089.19 1635.68,1084.74 1636.68,1080.32 1637.68,1075.95 1638.69,1071.61 1639.69,1067.3 \n",
       "  1640.7,1063.04 1641.7,1058.82 1642.71,1054.63 1643.71,1050.49 1644.71,1046.39 1645.72,1042.33 1646.72,1038.31 1647.73,1034.33 1648.73,1030.39 1649.74,1026.5 \n",
       "  1650.74,1022.65 1651.74,1018.84 1652.75,1015.08 1653.75,1011.36 1654.76,1007.68 1655.76,1004.05 1656.77,1000.46 1657.77,996.911 1658.78,993.408 1659.78,989.949 \n",
       "  1660.78,986.533 1661.79,983.161 1662.79,979.832 1663.8,976.547 1664.8,973.305 1665.81,970.107 1666.81,966.951 1667.81,963.838 1668.82,960.768 1669.82,957.741 \n",
       "  1670.83,954.756 1671.83,951.813 1672.84,948.912 1673.84,946.052 1674.85,943.234 1675.85,940.458 1676.85,937.722 1677.86,935.026 1678.86,932.371 1679.87,929.757 \n",
       "  1680.87,927.181 1681.88,924.646 1682.88,922.149 1683.88,919.691 1684.89,917.272 1685.89,914.89 1686.9,912.547 1687.9,910.24 1688.91,907.971 1689.91,905.739 \n",
       "  1690.91,903.543 1691.92,901.383 1692.92,899.258 1693.93,897.169 1694.93,895.115 1695.94,893.095 1696.94,891.11 1697.95,889.158 1698.95,887.24 1699.95,885.354 \n",
       "  1700.96,883.502 1701.96,881.681 1702.97,879.893 1703.97,878.136 1704.98,876.411 1705.98,874.716 1706.98,873.052 1707.99,871.418 1708.99,869.814 1710,868.24 \n",
       "  1711,866.694 1712.01,865.177 1713.01,863.689 1714.02,862.228 1715.02,860.795 1716.02,859.39 1717.03,858.012 1718.03,856.66 1719.04,855.335 1720.04,854.036 \n",
       "  1721.05,852.762 1722.05,851.514 1723.05,850.291 1724.06,849.093 1725.06,847.919 1726.07,846.77 1727.07,845.644 1728.08,844.542 1729.08,843.464 1730.08,842.408 \n",
       "  1731.09,841.375 1732.09,840.365 1733.1,839.377 1734.1,838.411 1735.11,837.466 1736.11,836.543 1737.12,835.642 1738.12,834.761 1739.12,833.9 1740.13,833.061 \n",
       "  1741.13,832.241 1742.14,831.442 1743.14,830.662 1744.15,829.902 1745.15,829.161 1746.15,828.44 1747.16,827.737 1748.16,827.053 1749.17,826.388 1750.17,825.741 \n",
       "  1751.18,825.112 1752.18,824.501 1753.18,823.908 1754.19,823.333 1755.19,822.775 1756.2,822.235 1757.2,821.711 1758.21,821.205 1759.21,820.716 1760.22,820.243 \n",
       "  1761.22,819.787 1762.22,819.347 1763.23,818.924 1764.23,818.517 1765.24,818.126 1766.24,817.751 1767.25,817.392 1768.25,817.048 1769.25,816.72 1770.26,816.408 \n",
       "  1771.26,816.111 1772.27,815.83 1773.27,815.564 1774.28,815.313 1775.28,815.077 1776.29,814.857 1777.29,814.651 1778.29,814.46 1779.3,814.285 1780.3,814.124 \n",
       "  1781.31,813.978 1782.31,813.846 1783.32,813.729 1784.32,813.627 1785.32,813.54 1786.33,813.467 1787.33,813.409 1788.34,813.365 1789.34,813.336 1790.35,813.322 \n",
       "  1791.35,813.322 1792.35,813.336 1793.36,813.365 1794.36,813.409 1795.37,813.467 1796.37,813.54 1797.38,813.628 1798.38,813.73 1799.39,813.847 1800.39,813.978 \n",
       "  1801.39,814.124 1802.4,814.285 1803.4,814.461 1804.41,814.652 1805.41,814.858 1806.42,815.078 1807.42,815.314 1808.42,815.565 1809.43,815.831 1810.43,816.113 \n",
       "  1811.44,816.409 1812.44,816.722 1813.45,817.049 1814.45,817.393 1815.46,817.752 1816.46,818.127 1817.46,818.518 1818.47,818.925 1819.47,819.349 1820.48,819.788 \n",
       "  1821.48,820.244 1822.49,820.717 1823.49,821.207 1824.49,821.713 1825.5,822.236 1826.5,822.777 1827.51,823.335 1828.51,823.91 1829.52,824.503 1830.52,825.114 \n",
       "  1831.52,825.742 1832.53,826.389 1833.53,827.055 1834.54,827.738 1835.54,828.441 1836.55,829.162 1837.55,829.903 1838.56,830.663 1839.56,831.443 1840.56,832.242 \n",
       "  1841.57,833.061 1842.57,833.901 1843.58,834.761 1844.58,835.642 1845.59,836.543 1846.59,837.466 1847.59,838.41 1848.6,839.376 1849.6,840.364 1850.61,841.374 \n",
       "  1851.61,842.407 1852.62,843.462 1853.62,844.54 1854.63,845.642 1855.63,846.767 1856.63,847.916 1857.64,849.09 1858.64,850.287 1859.65,851.51 1860.65,852.757 \n",
       "  1861.66,854.03 1862.66,855.329 1863.66,856.653 1864.67,858.004 1865.67,859.382 1866.68,860.787 1867.68,862.219 1868.69,863.678 1869.69,865.166 1870.69,866.682 \n",
       "  1871.7,868.227 1872.7,869.8 1873.71,871.403 1874.71,873.036 1875.72,874.699 1876.72,876.393 1877.73,878.117 1878.73,879.872 1879.73,881.659 1880.74,883.478 \n",
       "  1881.74,885.329 1882.75,887.212 1883.75,889.129 1884.76,891.079 1885.76,893.062 1886.76,895.08 1887.77,897.132 1888.77,899.219 1889.78,901.341 1890.78,903.499 \n",
       "  1891.79,905.692 1892.79,907.922 1893.79,910.188 1894.8,912.491 1895.8,914.832 1896.81,917.21 1897.81,919.626 1898.82,922.08 1899.82,924.573 1900.83,927.105 \n",
       "  1901.83,929.676 1902.83,932.287 1903.84,934.938 1904.84,937.628 1905.85,940.359 1906.85,943.131 1907.86,945.944 1908.86,948.797 1909.86,951.693 1910.87,954.63 \n",
       "  1911.87,957.609 1912.88,960.63 1913.88,963.693 1914.89,966.799 1915.89,969.947 1916.9,973.138 1917.9,976.372 1918.9,979.649 1919.91,982.969 1920.91,986.332 \n",
       "  1921.92,989.739 1922.92,993.188 1923.93,996.681 1924.93,1000.22 1925.93,1003.8 1926.94,1007.42 1927.94,1011.09 1928.95,1014.79 1929.95,1018.55 1930.96,1022.34 \n",
       "  1931.96,1026.18 1932.96,1030.05 1933.97,1033.98 1934.97,1037.94 1935.98,1041.94 1936.98,1045.99 1937.99,1050.07 1938.99,1054.2 1940,1058.37 1941,1062.57 \n",
       "  1942,1066.82 1943.01,1071.1 1944.01,1075.42 1945.02,1079.78 1946.02,1084.17 1947.03,1088.6 1948.03,1093.07 1949.03,1097.56 1950.04,1102.1 1951.04,1106.66 \n",
       "  1952.05,1111.26 1953.05,1115.89 1954.06,1120.54 1955.06,1125.23 1956.07,1129.94 1957.07,1134.68 1958.07,1139.44 1959.08,1144.23 1960.08,1149.04 1961.09,1153.88 \n",
       "  1962.09,1158.73 1963.1,1163.6 1964.1,1168.49 1965.1,1173.39 1966.11,1178.31 1967.11,1183.24 1968.12,1188.18 1969.12,1193.13 1970.13,1198.09 1971.13,1203.06 \n",
       "  1972.13,1208.02 1973.14,1212.99 1974.14,1217.96 1975.15,1222.93 1976.15,1227.9 1977.16,1232.86 1978.16,1237.81 1979.17,1242.75 1980.17,1247.68 1981.17,1252.6 \n",
       "  1982.18,1257.49 1983.18,1262.37 1984.19,1267.23 1985.19,1272.07 1986.2,1276.88 1987.2,1281.67 1988.2,1286.42 1989.21,1291.14 1990.21,1295.83 1991.22,1300.48 \n",
       "  1992.22,1305.09 1993.23,1309.65 1994.23,1314.18 1995.23,1318.65 1996.24,1323.08 1997.24,1327.46 1998.25,1331.78 1999.25,1336.04 2000.26,1340.24 2001.26,1344.39 \n",
       "  2002.27,1348.47 2003.27,1352.48 2004.27,1356.42 2005.28,1360.29 2006.28,1364.09 2007.29,1367.81 2008.29,1371.46 2009.3,1375.02 2010.3,1378.5 2011.3,1381.89 \n",
       "  2012.31,1385.2 2013.31,1388.42 2014.32,1391.55 2015.32,1394.58 2016.33,1397.52 2017.33,1400.35 2018.34,1403.09 2019.34,1405.73 2020.34,1408.27 2021.35,1410.7 \n",
       "  2022.35,1413.02 2023.36,1415.23 2024.36,1417.34 2025.37,1419.33 2026.37,1421.21 2027.37,1422.98 2028.38,1424.63 2029.38,1426.17 2030.39,1427.59 2031.39,1428.89 \n",
       "  2032.4,1430.07 2033.4,1431.13 2034.4,1432.06 2035.41,1432.88 2036.41,1433.58 2037.42,1434.15 2038.42,1434.6 2039.43,1434.92 2040.43,1435.12 2041.44,1435.2 \n",
       "  2042.44,1435.15 2043.44,1434.98 2044.45,1434.69 2045.45,1434.27 2046.46,1433.73 2047.46,1433.06 2048.47,1432.27 2049.47,1431.37 2050.47,1430.34 2051.48,1429.18 \n",
       "  2052.48,1427.91 2053.49,1426.53 2054.49,1425.02 2055.5,1423.39 2056.5,1421.66 2057.51,1419.8 2058.51,1417.84 2059.51,1415.76 2060.52,1413.57 2061.52,1411.27 \n",
       "  2062.53,1408.87 2063.53,1406.36 2064.54,1403.75 2065.54,1401.03 2066.54,1398.22 2067.55,1395.3 2068.55,1392.29 2069.56,1389.19 2070.56,1385.99 2071.57,1382.71 \n",
       "  2072.57,1379.33 2073.57,1375.87 2074.58,1372.33 2075.58,1368.71 2076.59,1365 2077.59,1361.22 2078.6,1357.37 2079.6,1353.44 2080.61,1349.45 2081.61,1345.38 \n",
       "  2082.61,1341.26 2083.62,1337.07 2084.62,1332.82 2085.63,1328.51 2086.63,1324.15 2087.64,1319.73 2088.64,1315.27 2089.64,1310.76 2090.65,1306.2 2091.65,1301.6 \n",
       "  2092.66,1296.96 2093.66,1292.28 2094.67,1287.57 2095.67,1282.82 2096.68,1278.04 2097.68,1273.24 2098.68,1268.41 2099.69,1263.55 2100.69,1258.68 2101.7,1253.78 \n",
       "  2102.7,1248.87 2103.71,1243.94 2104.71,1239 2105.71,1234.05 2106.72,1229.09 2107.72,1224.13 2108.73,1219.16 2109.73,1214.19 2110.74,1209.22 2111.74,1204.25 \n",
       "  2112.74,1199.28 2113.75,1194.32 2114.75,1189.37 2115.76,1184.43 2116.76,1179.49 2117.77,1174.57 2118.77,1169.66 2119.78,1164.77 2120.78,1159.89 2121.78,1155.03 \n",
       "  2122.79,1150.2 2123.79,1145.38 2124.8,1140.58 2125.8,1135.81 2126.81,1131.07 2127.81,1126.35 2128.81,1121.65 2129.82,1116.99 2130.82,1112.35 2131.83,1107.75 \n",
       "  2132.83,1103.17 2133.84,1098.63 2134.84,1094.13 2135.84,1089.65 2136.85,1085.21 2137.85,1080.81 2138.86,1076.44 2139.86,1072.11 2140.87,1067.82 2141.87,1063.56 \n",
       "  2142.88,1059.35 2143.88,1055.17 2144.88,1051.03 2145.89,1046.94 2146.89,1042.88 2147.9,1038.86 2148.9,1034.89 2149.91,1030.96 2150.91,1027.07 2151.91,1023.22 \n",
       "  2152.92,1019.41 2153.92,1015.65 2154.93,1011.93 2155.93,1008.25 2156.94,1004.62 2157.94,1001.03 2158.95,997.481 2159.95,993.976 2160.95,990.515 2161.96,987.096 \n",
       "  2162.96,983.721 2163.97,980.389 2164.97,977.101 2165.98,973.855 2166.98,970.652 2167.98,967.492 2168.99,964.375 2169.99,961.3 2171,958.267 2172,955.276 \n",
       "  2173.01,952.328 2174.01,949.421 2175.01,946.555 2176.02,943.731 2177.02,940.948 2178.03,938.206 2179.03,935.504 2180.04,932.842 2181.04,930.22 2182.05,927.637 \n",
       "  2183.05,925.094 2184.05,922.59 2185.06,920.125 2186.06,917.698 2187.07,915.309 2188.07,912.957 2189.08,910.643 2190.08,908.366 2191.08,906.126 2192.09,903.921 \n",
       "  2193.09,901.753 2194.1,899.621 2195.1,897.523 2196.11,895.46 2197.11,893.432 2198.12,891.438 2199.12,889.478 2200.12,887.551 2201.13,885.658 2202.13,883.796 \n",
       "  2203.14,881.968 2204.14,880.171 2205.15,878.405 2206.15,876.671 2207.15,874.968 2208.16,873.295 2209.16,871.653 2210.17,870.04 2211.17,868.456 2212.18,866.902 \n",
       "  2213.18,865.376 2214.18,863.879 2215.19,862.41 2216.19,860.969 2217.2,859.554 2218.2,858.167 2219.21,856.807 2220.21,855.473 2221.22,854.165 2222.22,852.883 \n",
       "  2223.22,851.626 2224.23,850.394 2225.23,849.187 2226.24,848.004 2227.24,846.846 2228.25,845.712 2229.25,844.601 2230.25,843.513 2231.26,842.449 2232.26,841.407 \n",
       "  2233.27,840.388 2234.27,839.39 2235.28,838.415 2236.28,837.462 2237.28,836.53 2238.29,835.619 2239.29,834.729 2240.3,833.86 2241.3,833.011 2242.31,832.182 \n",
       "  2243.31,831.373 2244.32,830.584 2245.32,829.815 2246.32,829.065 2247.33,828.334 2248.33,827.622 2249.34,826.928 2250.34,826.253 2251.35,825.597 2252.35,824.958 \n",
       "  2253.35,824.338 2254.36,823.735 2255.36,823.15 2256.37,822.582 2257.37,822.032 2258.38,821.498 2259.38,820.982 2260.39,820.482 2261.39,819.999 2262.39,819.533 \n",
       "  2263.4,819.083 2264.4,818.649 2265.41,818.231 2266.41,817.829 2267.42,817.444 2268.42,817.073 2269.42,816.719 2270.43,816.38 2271.43,816.057 2272.44,815.749 \n",
       "  2273.44,815.456 2274.45,815.178 2275.45,814.916 2276.45,814.668 2277.46,814.435 2278.46,814.218 2279.47,814.015 2280.47,813.827 2281.48,813.653 2282.48,813.494 \n",
       "  2283.49,813.35 2284.49,813.22 2285.49,813.105 2286.5,813.004 2287.5,812.918 2288.51,812.846 2289.51,812.789 2290.52,812.746 2291.52,812.717 2292.52,812.703 \n",
       "  \n",
       "  \"/>\n",
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       "  284.815,766.439 285.82,765.625 286.824,764.811 287.828,763.996 288.833,763.181 289.837,762.364 290.841,761.546 291.846,760.726 292.85,759.904 293.854,759.08 \n",
       "  294.859,758.254 295.863,757.425 296.868,756.593 297.872,755.758 298.876,754.919 299.881,754.077 300.885,753.23 301.889,752.38 302.894,751.524 303.898,750.665 \n",
       "  304.902,749.8 305.907,748.929 306.911,748.054 307.915,747.172 308.92,746.284 309.924,745.39 310.929,744.489 311.933,743.581 312.937,742.666 313.942,741.744 \n",
       "  314.946,740.813 315.95,739.875 316.955,738.928 317.959,737.973 318.963,737.008 319.968,736.035 320.972,735.052 321.976,734.059 322.981,733.056 323.985,732.042 \n",
       "  324.99,731.018 325.994,729.983 326.998,728.936 328.003,727.878 329.007,726.807 330.011,725.725 331.016,724.63 332.02,723.522 333.024,722.4 334.029,721.265 \n",
       "  335.033,720.116 336.037,718.953 337.042,717.775 338.046,716.583 339.051,715.375 340.055,714.151 341.059,712.912 342.064,711.656 343.068,710.383 344.072,709.093 \n",
       "  345.077,707.786 346.081,706.462 347.085,705.119 348.09,703.757 349.094,702.377 350.098,700.978 351.103,699.558 352.107,698.119 353.112,696.66 354.116,695.179 \n",
       "  355.12,693.678 356.125,692.155 357.129,690.61 358.133,689.042 359.138,687.452 360.142,685.839 361.146,684.202 362.151,682.541 363.155,680.856 364.159,679.146 \n",
       "  365.164,677.411 366.168,675.65 367.173,673.863 368.177,672.05 369.181,670.209 370.186,668.342 371.19,666.447 372.194,664.523 373.199,662.571 374.203,660.59 \n",
       "  375.207,658.58 376.212,656.54 377.216,654.469 378.22,652.368 379.225,650.236 380.229,648.072 381.234,645.876 382.238,643.648 383.242,641.387 384.247,639.093 \n",
       "  385.251,636.766 386.255,634.404 387.26,632.008 388.264,629.577 389.268,627.11 390.273,624.609 391.277,622.071 392.281,619.497 393.286,616.886 394.29,614.238 \n",
       "  395.295,611.552 396.299,608.829 397.303,606.067 398.308,603.267 399.312,600.428 400.316,597.549 401.321,594.632 402.325,591.674 403.329,588.676 404.334,585.638 \n",
       "  405.338,582.56 406.342,579.44 407.347,576.28 408.351,573.078 409.356,569.834 410.36,566.549 411.364,563.221 412.369,559.852 413.373,556.441 414.377,552.987 \n",
       "  415.382,549.491 416.386,545.952 417.39,542.37 418.395,538.746 419.399,535.08 420.403,531.371 421.408,527.619 422.412,523.825 423.417,519.988 424.421,516.109 \n",
       "  425.425,512.188 426.43,508.225 427.434,504.22 428.438,500.173 429.443,496.085 430.447,491.957 431.451,487.787 432.456,483.577 433.46,479.328 434.464,475.039 \n",
       "  435.469,470.711 436.473,466.344 437.478,461.94 438.482,457.498 439.486,453.019 440.491,448.505 441.495,443.955 442.499,439.37 443.504,434.751 444.508,430.1 \n",
       "  445.512,425.416 446.517,420.702 447.521,415.957 448.525,411.182 449.53,406.38 450.534,401.55 451.539,396.695 452.543,391.815 453.547,386.911 454.552,381.985 \n",
       "  455.556,377.038 456.56,372.072 457.565,367.088 458.569,362.087 459.573,357.07 460.578,352.041 461.582,346.999 462.586,341.947 463.591,336.886 464.595,331.819 \n",
       "  465.599,326.746 466.604,321.67 467.608,316.593 468.613,311.517 469.617,306.443 470.621,301.373 471.626,296.31 472.63,291.256 473.634,286.212 474.639,281.181 \n",
       "  475.643,276.166 476.647,271.167 477.652,266.188 478.656,261.231 479.66,256.298 480.665,251.392 481.669,246.514 482.674,241.668 483.678,236.855 484.682,232.078 \n",
       "  485.687,227.34 486.691,222.642 487.695,217.988 488.7,213.38 489.704,208.82 490.708,204.311 491.713,199.855 492.717,195.455 493.721,191.113 494.726,186.832 \n",
       "  495.73,182.614 496.735,178.462 497.739,174.379 498.743,170.366 499.748,166.425 500.752,162.561 501.756,158.774 502.761,155.067 503.765,151.443 504.769,147.903 \n",
       "  505.774,144.451 506.778,141.088 507.782,137.816 508.787,134.638 509.791,131.555 510.796,128.57 511.8,125.685 512.804,122.901 513.809,120.22 514.813,117.645 \n",
       "  515.817,115.177 516.822,112.817 517.826,110.568 518.83,108.431 519.835,106.406 520.839,104.497 521.843,102.703 522.848,101.027 523.852,99.4696 524.857,98.0314 \n",
       "  525.861,96.7138 526.865,95.5177 527.87,94.4439 528.874,93.4932 529.878,92.6662 530.883,91.9636 531.887,91.3857 532.891,90.9331 533.896,90.6061 534.9,90.4048 \n",
       "  535.904,90.3294 536.909,90.3799 537.913,90.5563 538.918,90.8584 539.922,91.286 540.926,91.8388 541.931,92.5164 542.935,93.3182 543.939,94.2437 544.944,95.2921 \n",
       "  545.948,96.4628 546.952,97.7548 547.957,99.1673 548.961,100.699 549.965,102.349 550.97,104.117 551.974,106 552.979,107.997 553.983,110.108 554.987,112.33 \n",
       "  555.992,114.663 556.996,117.104 558,119.651 559.005,122.304 560.009,125.06 561.013,127.917 562.018,130.873 563.022,133.927 564.026,137.076 565.031,140.318 \n",
       "  566.035,143.651 567.04,147.074 568.044,150.583 569.048,154.176 570.053,157.852 571.057,161.607 572.061,165.44 573.066,169.348 574.07,173.328 575.074,177.379 \n",
       "  576.079,181.498 577.083,185.682 578.087,189.929 579.092,194.236 580.096,198.602 581.101,203.022 582.105,207.496 583.109,212.02 584.114,216.592 585.118,221.209 \n",
       "  586.122,225.869 587.127,230.57 588.131,235.309 589.135,240.083 590.14,244.891 591.144,249.729 592.148,254.596 593.153,259.489 594.157,264.405 595.162,269.343 \n",
       "  596.166,274.3 597.17,279.274 598.175,284.262 599.179,289.263 600.183,294.274 601.188,299.293 602.192,304.318 603.196,309.347 604.201,314.379 605.205,319.41 \n",
       "  606.209,324.44 607.214,329.465 608.218,334.486 609.223,339.499 610.227,344.502 611.231,349.495 612.236,354.476 613.24,359.442 614.244,364.393 615.249,369.327 \n",
       "  616.253,374.242 617.257,379.137 618.262,384.01 619.266,388.861 620.27,393.687 621.275,398.488 622.279,403.263 623.284,408.01 624.288,412.728 625.292,417.417 \n",
       "  626.297,422.074 627.301,426.7 628.305,431.292 629.31,435.852 630.314,440.376 631.318,444.865 632.323,449.319 633.327,453.735 634.331,458.114 635.336,462.455 \n",
       "  636.34,466.757 637.345,471.02 638.349,475.243 639.353,479.426 640.358,483.568 641.362,487.669 642.366,491.728 643.371,495.745 644.375,499.721 645.379,503.653 \n",
       "  646.384,507.543 647.388,511.391 648.392,515.194 649.397,518.955 650.401,522.672 651.406,526.346 652.41,529.975 653.414,533.562 654.419,537.104 655.423,540.602 \n",
       "  656.427,544.057 657.432,547.468 658.436,550.836 659.44,554.16 660.445,557.44 661.449,560.677 662.453,563.87 663.458,567.021 664.462,570.128 665.467,573.193 \n",
       "  666.471,576.215 667.475,579.195 668.48,582.132 669.484,585.028 670.488,587.881 671.493,590.694 672.497,593.465 673.501,596.195 674.506,598.885 675.51,601.534 \n",
       "  676.514,604.143 677.519,606.712 678.523,609.242 679.528,611.733 680.532,614.185 681.536,616.599 682.541,618.975 683.545,621.313 684.549,623.613 685.554,625.876 \n",
       "  686.558,628.103 687.562,630.293 688.567,632.448 689.571,634.567 690.575,636.65 691.58,638.699 692.584,640.713 693.589,642.693 694.593,644.639 695.597,646.552 \n",
       "  696.602,648.431 697.606,650.278 698.61,652.093 699.615,653.876 700.619,655.627 701.623,657.347 702.628,659.036 703.632,660.695 704.636,662.324 705.641,663.922 \n",
       "  706.645,665.492 707.65,667.032 708.654,668.544 709.658,670.027 710.663,671.482 711.667,672.91 712.671,674.31 713.676,675.683 714.68,677.03 715.684,678.35 \n",
       "  716.689,679.644 717.693,680.912 718.697,682.155 719.702,683.373 720.706,684.566 721.71,685.735 722.715,686.88 723.719,688 724.724,689.097 725.728,690.171 \n",
       "  726.732,691.221 727.737,692.249 728.741,693.255 729.745,694.238 730.75,695.199 731.754,696.139 732.758,697.057 733.763,697.954 734.767,698.83 735.771,699.685 \n",
       "  736.776,700.52 737.78,701.334 738.785,702.129 739.789,702.903 740.793,703.659 741.798,704.394 742.802,705.111 743.806,705.809 744.811,706.487 745.815,707.148 \n",
       "  746.819,707.79 747.824,708.413 748.828,709.019 749.832,709.607 750.837,710.177 751.841,710.73 752.846,711.265 753.85,711.783 754.854,712.284 755.859,712.768 \n",
       "  756.863,713.236 757.867,713.686 758.872,714.12 759.876,714.538 760.88,714.94 761.885,715.325 762.889,715.695 763.893,716.048 764.898,716.386 765.902,716.708 \n",
       "  766.907,717.014 767.911,717.305 768.915,717.581 769.92,717.841 770.924,718.086 771.928,718.315 772.933,718.53 773.937,718.729 774.941,718.913 775.946,719.083 \n",
       "  776.95,719.237 777.954,719.377 778.959,719.502 779.963,719.612 780.968,719.707 781.972,719.787 782.976,719.853 783.981,719.904 784.985,719.941 785.989,719.963 \n",
       "  786.994,719.97 787.998,719.962 789.002,719.94 790.007,719.904 791.011,719.852 792.015,719.786 793.02,719.705 794.024,719.61 795.029,719.5 796.033,719.374 \n",
       "  797.037,719.235 798.042,719.08 799.046,718.91 800.05,718.726 801.055,718.526 802.059,718.311 803.063,718.081 804.068,717.836 805.072,717.576 806.076,717.3 \n",
       "  807.081,717.009 808.085,716.703 809.09,716.38 810.094,716.042 811.098,715.689 812.103,715.319 813.107,714.933 814.111,714.531 815.116,714.113 816.12,713.679 \n",
       "  817.124,713.228 818.129,712.76 819.133,712.276 820.137,711.775 821.142,711.256 822.146,710.721 823.151,710.168 824.155,709.598 825.159,709.01 826.164,708.404 \n",
       "  827.168,707.78 828.172,707.138 829.177,706.477 830.181,705.798 831.185,705.1 832.19,704.383 833.194,703.647 834.198,702.892 835.203,702.117 836.207,701.323 \n",
       "  837.212,700.508 838.216,699.673 839.22,698.818 840.225,697.942 841.229,697.045 842.233,696.126 843.238,695.187 844.242,694.225 845.246,693.242 846.251,692.237 \n",
       "  847.255,691.209 848.259,690.158 849.264,689.084 850.268,687.987 851.273,686.867 852.277,685.722 853.281,684.554 854.286,683.361 855.29,682.143 856.294,680.9 \n",
       "  857.299,679.632 858.303,678.338 859.307,677.018 860.312,675.672 861.316,674.299 862.32,672.899 863.325,671.472 864.329,670.017 865.334,668.534 866.338,667.023 \n",
       "  867.342,665.483 868.347,663.914 869.351,662.316 870.355,660.688 871.36,659.03 872.364,657.342 873.368,655.623 874.373,653.872 875.377,652.09 876.381,650.277 \n",
       "  877.386,648.431 878.39,646.552 879.395,644.641 880.399,642.696 881.403,640.717 882.408,638.705 883.412,636.657 884.416,634.576 885.421,632.459 886.425,630.306 \n",
       "  887.429,628.118 888.434,625.893 889.438,623.632 890.442,621.334 891.447,618.999 892.451,616.626 893.456,614.215 894.46,611.765 895.464,609.278 896.469,606.751 \n",
       "  897.473,604.185 898.477,601.579 899.482,598.934 900.486,596.248 901.49,593.522 902.495,590.755 903.499,587.947 904.503,585.098 905.508,582.208 906.512,579.275 \n",
       "  907.517,576.301 908.521,573.285 909.525,570.226 910.53,567.125 911.534,563.981 912.538,560.794 913.543,557.564 914.547,554.291 915.551,550.975 916.556,547.615 \n",
       "  917.56,544.213 918.564,540.766 919.569,537.277 920.573,533.744 921.578,530.168 922.582,526.548 923.586,522.885 924.591,519.179 925.595,515.43 926.599,511.638 \n",
       "  927.604,507.803 928.608,503.926 929.612,500.006 930.617,496.045 931.621,492.042 932.625,487.997 933.63,483.911 934.634,479.785 935.639,475.619 936.643,471.413 \n",
       "  937.647,467.168 938.652,462.884 939.656,458.562 940.66,454.202 941.665,449.806 942.669,445.374 943.673,440.906 944.678,436.403 945.682,431.867 946.686,427.298 \n",
       "  947.691,422.697 948.695,418.064 949.7,413.402 950.704,408.71 951.708,403.991 952.713,399.244 953.717,394.472 954.721,389.675 955.726,384.855 956.73,380.013 \n",
       "  957.734,375.151 958.739,370.269 959.743,365.37 960.747,360.454 961.752,355.524 962.756,350.58 963.76,345.625 964.765,340.66 965.769,335.686 966.774,330.707 \n",
       "  967.778,325.722 968.782,320.735 969.787,315.747 970.791,310.761 971.795,305.777 972.8,300.798 973.804,295.826 974.808,290.863 975.813,285.912 976.817,280.974 \n",
       "  977.821,276.051 978.826,271.147 979.83,266.262 980.835,261.4 981.839,256.562 982.843,251.752 983.848,246.97 984.852,242.221 985.856,237.505 986.861,232.826 \n",
       "  987.865,228.186 988.869,223.587 989.874,219.032 990.878,214.523 991.882,210.063 992.887,205.655 993.891,201.3 994.896,197.001 995.9,192.76 996.904,188.581 \n",
       "  997.909,184.466 998.913,180.416 999.917,176.435 1000.92,172.525 1001.93,168.688 1002.93,164.927 1003.93,161.243 1004.94,157.64 1005.94,154.12 1006.95,150.684 \n",
       "  1007.95,147.336 1008.96,144.076 1009.96,140.908 1010.97,137.834 1011.97,134.855 1012.97,131.973 1013.98,129.191 1014.98,126.511 1015.99,123.933 1016.99,121.461 \n",
       "  1018,119.095 1019,116.837 1020,114.69 1021.01,112.654 1022.01,110.73 1023.02,108.921 1024.02,107.227 1025.03,105.65 1026.03,104.191 1027.03,102.851 \n",
       "  1028.04,101.631 1029.04,100.531 1030.05,99.5528 1031.05,98.697 1032.06,97.9641 1033.06,97.3547 1034.07,96.8691 1035.07,96.5078 1036.07,96.2711 1037.08,96.1591 \n",
       "  1038.08,96.1719 1039.09,96.3096 1040.09,96.572 1041.1,96.959 1042.1,97.4703 1043.1,98.1056 1044.11,98.8644 1045.11,99.7462 1046.12,100.75 1047.12,101.876 \n",
       "  1048.13,103.123 1049.13,104.489 1050.14,105.975 1051.14,107.579 1052.14,109.299 1053.15,111.135 1054.15,113.086 1055.16,115.149 1056.16,117.325 1057.17,119.61 \n",
       "  1058.17,122.004 1059.17,124.504 1060.18,127.11 1061.18,129.82 1062.19,132.631 1063.19,135.541 1064.2,138.55 1065.2,141.654 1066.2,144.852 1067.21,148.142 \n",
       "  1068.21,151.521 1069.22,154.987 1070.22,158.539 1071.23,162.174 1072.23,165.889 1073.24,169.683 1074.24,173.552 1075.24,177.496 1076.25,181.51 1077.25,185.593 \n",
       "  1078.26,189.743 1079.26,193.956 1080.27,198.231 1081.27,202.565 1082.27,206.956 1083.28,211.4 1084.28,215.897 1085.29,220.442 1086.29,225.034 1087.3,229.67 \n",
       "  1088.3,234.348 1089.31,239.066 1090.31,243.82 1091.31,248.609 1092.32,253.43 1093.32,258.281 1094.33,263.159 1095.33,268.062 1096.34,272.988 1097.34,277.934 \n",
       "  1098.34,282.899 1099.35,287.88 1100.35,292.874 1101.36,297.88 1102.36,302.896 1103.37,307.919 1104.37,312.948 1105.37,317.981 1106.38,323.014 1107.38,328.048 \n",
       "  1108.39,333.079 1109.39,338.106 1110.4,343.127 1111.4,348.14 1112.41,353.144 1113.41,358.137 1114.41,363.118 1115.42,368.084 1116.42,373.034 1117.43,377.967 \n",
       "  1118.43,382.882 1119.44,387.776 1120.44,392.65 1121.44,397.5 1122.45,402.326 1123.45,407.128 1124.46,411.903 1125.46,416.651 1126.47,421.37 1127.47,426.06 \n",
       "  1128.48,430.719 1129.48,435.347 1130.48,439.942 1131.49,444.505 1132.49,449.033 1133.5,453.527 1134.5,457.986 1135.51,462.408 1136.51,466.794 1137.51,471.142 \n",
       "  1138.52,475.453 1139.52,479.725 1140.53,483.958 1141.53,488.152 1142.54,492.306 1143.54,496.42 1144.54,500.493 1145.55,504.526 1146.55,508.518 1147.56,512.468 \n",
       "  1148.56,516.377 1149.57,520.244 1150.57,524.069 1151.58,527.852 1152.58,531.593 1153.58,535.292 1154.59,538.949 1155.59,542.564 1156.6,546.136 1157.6,549.666 \n",
       "  1158.61,553.154 1159.61,556.6 1160.61,560.004 1161.62,563.365 1162.62,566.686 1163.63,569.964 1164.63,573.201 1165.64,576.397 1166.64,579.551 1167.64,582.665 \n",
       "  1168.65,585.738 1169.65,588.771 1170.66,591.764 1171.66,594.717 1172.67,597.63 1173.67,600.504 1174.68,603.339 1175.68,606.135 1176.68,608.893 1177.69,611.612 \n",
       "  1178.69,614.294 1179.7,616.939 1180.7,619.547 1181.71,622.118 1182.71,624.653 1183.71,627.152 1184.72,629.616 1185.72,632.044 1186.73,634.438 1187.73,636.798 \n",
       "  1188.74,639.123 1189.74,641.415 1190.75,643.674 1191.75,645.901 1192.75,648.095 1193.76,650.257 1194.76,652.388 1195.77,654.487 1196.77,656.556 1197.78,658.595 \n",
       "  1198.78,660.604 1199.78,662.584 1200.79,664.535 1201.79,666.457 1202.8,668.352 1203.8,670.218 1204.81,672.058 1205.81,673.87 1206.81,675.656 1207.82,677.417 \n",
       "  1208.82,679.151 1209.83,680.86 1210.83,682.545 1211.84,684.205 1212.84,685.842 1213.85,687.455 1214.85,689.044 1215.85,690.611 1216.86,692.156 1217.86,693.679 \n",
       "  1218.87,695.18 1219.87,696.66 1220.88,698.119 1221.88,699.558 1222.88,700.977 1223.89,702.376 1224.89,703.756 1225.9,705.118 1226.9,706.46 1227.91,707.785 \n",
       "  1228.91,709.092 1229.92,710.381 1230.92,711.654 1231.92,712.91 1232.93,714.149 1233.93,715.373 1234.94,716.581 1235.94,717.773 1236.95,718.951 1237.95,720.114 \n",
       "  1238.95,721.263 1239.96,722.398 1240.96,723.519 1241.97,724.627 1242.97,725.723 1243.98,726.805 1244.98,727.875 1245.98,728.934 1246.99,729.98 1247.99,731.016 \n",
       "  1249,732.04 1250,733.053 1251.01,734.057 1252.01,735.05 1253.02,736.033 1254.02,737.006 1255.02,737.971 1256.03,738.926 1257.03,739.873 1258.04,740.812 \n",
       "  1259.04,741.742 1260.05,742.665 1261.05,743.58 1262.05,744.487 1263.06,745.388 1264.06,746.283 1265.07,747.17 1266.07,748.052 1267.08,748.928 1268.08,749.798 \n",
       "  1269.08,750.663 1270.09,751.523 1271.09,752.379 1272.1,753.229 1273.1,754.076 1274.11,754.918 1275.11,755.757 1276.12,756.592 1277.12,757.424 1278.12,758.253 \n",
       "  1279.13,759.08 1280.13,759.904 1281.14,760.725 1282.14,761.545 1283.15,762.364 1284.15,763.181 1285.15,763.996 1286.16,764.811 1287.16,765.625 1288.17,766.439 \n",
       "  1289.17,767.253 1290.18,768.067 1291.18,768.881 1292.19,769.696 1293.19,770.511 1294.19,771.328 1295.2,772.147 1296.2,772.967 1297.21,773.788 1298.21,774.612 \n",
       "  1299.22,775.439 1300.22,776.268 1301.22,777.1 1302.23,777.935 1303.23,778.774 1304.24,779.616 1305.24,780.463 1306.25,781.313 1307.25,782.169 1308.25,783.029 \n",
       "  1309.26,783.894 1310.26,784.764 1311.27,785.64 1312.27,786.521 1313.28,787.409 1314.28,788.304 1315.29,789.205 1316.29,790.112 1317.29,791.027 1318.3,791.95 \n",
       "  1319.3,792.88 1320.31,793.819 1321.31,794.766 1322.32,795.721 1323.32,796.686 1324.32,797.659 1325.33,798.642 1326.33,799.635 1327.34,800.639 1328.34,801.652 \n",
       "  1329.35,802.676 1330.35,803.712 1331.36,804.758 1332.36,805.817 1333.36,806.887 1334.37,807.969 1335.37,809.065 1336.38,810.173 1337.38,811.294 1338.39,812.429 \n",
       "  1339.39,813.578 1340.39,814.741 1341.4,815.919 1342.4,817.111 1343.41,818.319 1344.41,819.543 1345.42,820.782 1346.42,822.038 1347.42,823.311 1348.43,824.6 \n",
       "  1349.43,825.907 1350.44,827.232 1351.44,828.574 1352.45,829.936 1353.45,831.316 1354.46,832.715 1355.46,834.134 1356.46,835.573 1357.47,837.032 1358.47,838.512 \n",
       "  1359.48,840.013 1360.48,841.536 1361.49,843.081 1362.49,844.648 1363.49,846.237 1364.5,847.85 1365.5,849.487 1366.51,851.147 1367.51,852.831 1368.52,854.541 \n",
       "  1369.52,856.275 1370.53,858.036 1371.53,859.822 1372.53,861.634 1373.54,863.474 1374.54,865.34 1375.55,867.235 1376.55,869.157 1377.56,871.108 1378.56,873.088 \n",
       "  1379.56,875.097 1380.57,877.136 1381.57,879.205 1382.58,881.304 1383.58,883.435 1384.59,885.597 1385.59,887.791 1386.59,890.018 1387.6,892.277 1388.6,894.569 \n",
       "  1389.61,896.894 1390.61,899.254 1391.62,901.648 1392.62,904.076 1393.63,906.54 1394.63,909.039 1395.63,911.574 1396.64,914.145 1397.64,916.753 1398.65,919.398 \n",
       "  1399.65,922.08 1400.66,924.799 1401.66,927.557 1402.66,930.353 1403.67,933.188 1404.67,936.062 1405.68,938.975 1406.68,941.928 1407.69,944.921 1408.69,947.954 \n",
       "  1409.69,951.027 1410.7,954.14 1411.7,957.295 1412.71,960.491 1413.71,963.728 1414.72,967.006 1415.72,970.327 1416.73,973.688 1417.73,977.092 1418.73,980.538 \n",
       "  1419.74,984.026 1420.74,987.556 1421.75,991.128 1422.75,994.743 1423.76,998.4 1424.76,1002.1 1425.76,1005.84 1426.77,1009.62 1427.77,1013.45 1428.78,1017.32 \n",
       "  1429.78,1021.22 1430.79,1025.17 1431.79,1029.17 1432.8,1033.2 1433.8,1037.27 1434.8,1041.39 1435.81,1045.54 1436.81,1049.73 1437.82,1053.97 1438.82,1058.24 \n",
       "  1439.83,1062.55 1440.83,1066.9 1441.83,1071.28 1442.84,1075.71 1443.84,1080.16 1444.85,1084.66 1445.85,1089.19 1446.86,1093.75 1447.86,1098.35 1448.86,1102.97 \n",
       "  1449.87,1107.63 1450.87,1112.32 1451.88,1117.04 1452.88,1121.79 1453.89,1126.56 1454.89,1131.37 1455.9,1136.19 1456.9,1141.04 1457.9,1145.92 1458.91,1150.81 \n",
       "  1459.91,1155.72 1460.92,1160.66 1461.92,1165.61 1462.93,1170.57 1463.93,1175.55 1464.93,1180.55 1465.94,1185.55 1466.94,1190.57 1467.95,1195.59 1468.95,1200.61 \n",
       "  1469.96,1205.64 1470.96,1210.68 1471.97,1215.71 1472.97,1220.74 1473.97,1225.77 1474.98,1230.8 1475.98,1235.81 1476.99,1240.82 1477.99,1245.81 1479,1250.79 \n",
       "  1480,1255.76 1481,1260.7 1482.01,1265.63 1483.01,1270.53 1484.02,1275.41 1485.02,1280.26 1486.03,1285.08 1487.03,1289.87 1488.03,1294.63 1489.04,1299.34 \n",
       "  1490.04,1304.02 1491.05,1308.66 1492.05,1313.25 1493.06,1317.8 1494.06,1322.29 1495.07,1326.74 1496.07,1331.13 1497.07,1335.46 1498.08,1339.74 1499.08,1343.95 \n",
       "  1500.09,1348.1 1501.09,1352.18 1502.1,1356.2 1503.1,1360.14 1504.1,1364.01 1505.11,1367.8 1506.11,1371.52 1507.12,1375.15 1508.12,1378.7 1509.13,1382.17 \n",
       "  1510.13,1385.55 1511.13,1388.84 1512.14,1392.04 1513.14,1395.14 1514.15,1398.15 1515.15,1401.06 1516.16,1403.87 1517.16,1406.58 1518.17,1409.19 1519.17,1411.69 \n",
       "  1520.17,1414.08 1521.18,1416.37 1522.18,1418.54 1523.19,1420.61 1524.19,1422.56 1525.2,1424.39 1526.2,1426.11 1527.2,1427.72 1528.21,1429.2 1529.21,1430.57 \n",
       "  1530.22,1431.82 1531.22,1432.94 1532.23,1433.95 1533.23,1434.83 1534.24,1435.59 1535.24,1436.22 1536.24,1436.73 1537.25,1437.12 1538.25,1437.38 1539.26,1437.52 \n",
       "  1540.26,1437.53 1541.27,1437.42 1542.27,1437.18 1543.27,1436.82 1544.28,1436.34 1545.28,1435.73 1546.29,1434.99 1547.29,1434.14 1548.3,1433.16 1549.3,1432.06 \n",
       "  1550.3,1430.84 1551.31,1429.5 1552.31,1428.04 1553.32,1426.46 1554.32,1424.77 1555.33,1422.96 1556.33,1421.04 1557.34,1419 1558.34,1416.85 1559.34,1414.6 \n",
       "  1560.35,1412.23 1561.35,1409.76 1562.36,1407.18 1563.36,1404.5 1564.37,1401.72 1565.37,1398.84 1566.37,1395.86 1567.38,1392.78 1568.38,1389.62 1569.39,1386.36 \n",
       "  1570.39,1383.01 1571.4,1379.57 1572.4,1376.05 1573.41,1372.45 1574.41,1368.77 1575.41,1365 1576.42,1361.17 1577.42,1357.26 1578.43,1353.28 1579.43,1349.23 \n",
       "  1580.44,1345.11 1581.44,1340.93 1582.44,1336.69 1583.45,1332.39 1584.45,1328.04 1585.46,1323.63 1586.46,1319.17 1587.47,1314.66 1588.47,1310.11 1589.47,1305.51 \n",
       "  1590.48,1300.87 1591.48,1296.19 1592.49,1291.47 1593.49,1286.72 1594.5,1281.94 1595.5,1277.13 1596.51,1272.29 1597.51,1267.43 1598.51,1262.55 1599.52,1257.64 \n",
       "  1600.52,1252.72 1601.53,1247.78 1602.53,1242.83 1603.54,1237.87 1604.54,1232.89 1605.54,1227.92 1606.55,1222.93 1607.55,1217.94 1608.56,1212.96 1609.56,1207.97 \n",
       "  1610.57,1202.99 1611.57,1198.01 1612.58,1193.03 1613.58,1188.07 1614.58,1183.11 1615.59,1178.17 1616.59,1173.24 1617.6,1168.32 1618.6,1163.42 1619.61,1158.54 \n",
       "  1620.61,1153.68 1621.61,1148.84 1622.62,1144.02 1623.62,1139.22 1624.63,1134.45 1625.63,1129.7 1626.64,1124.98 1627.64,1120.29 1628.64,1115.63 1629.65,1111 \n",
       "  1630.65,1106.39 1631.66,1101.82 1632.66,1097.29 1633.67,1092.79 1634.67,1088.32 1635.68,1083.89 1636.68,1079.49 1637.68,1075.13 1638.69,1070.81 1639.69,1066.52 \n",
       "  1640.7,1062.28 1641.7,1058.07 1642.71,1053.91 1643.71,1049.78 1644.71,1045.69 1645.72,1041.65 1646.72,1037.65 1647.73,1033.69 1648.73,1029.77 1649.74,1025.89 \n",
       "  1650.74,1022.05 1651.74,1018.26 1652.75,1014.51 1653.75,1010.81 1654.76,1007.14 1655.76,1003.52 1656.77,999.948 1657.77,996.415 1658.78,992.926 1659.78,989.479 \n",
       "  1660.78,986.077 1661.79,982.717 1662.79,979.401 1663.8,976.128 1664.8,972.898 1665.81,969.711 1666.81,966.567 1667.81,963.466 1668.82,960.407 1669.82,957.391 \n",
       "  1670.83,954.417 1671.83,951.484 1672.84,948.594 1673.84,945.745 1674.85,942.937 1675.85,940.17 1676.85,937.444 1677.86,934.758 1678.86,932.113 1679.87,929.507 \n",
       "  1680.87,926.941 1681.88,924.414 1682.88,921.926 1683.88,919.477 1684.89,917.066 1685.89,914.693 1686.9,912.358 1687.9,910.06 1688.91,907.799 1689.91,905.574 \n",
       "  1690.91,903.386 1691.92,901.233 1692.92,899.116 1693.93,897.034 1694.93,894.987 1695.94,892.975 1696.94,890.996 1697.95,889.051 1698.95,887.14 1699.95,885.261 \n",
       "  1700.96,883.415 1701.96,881.602 1702.97,879.82 1703.97,878.069 1704.98,876.35 1705.98,874.662 1706.98,873.004 1707.99,871.376 1708.99,869.778 1710,868.209 \n",
       "  1711,866.669 1712.01,865.158 1713.01,863.675 1714.02,862.22 1715.02,860.793 1716.02,859.393 1717.03,858.02 1718.03,856.674 1719.04,855.354 1720.04,854.06 \n",
       "  1721.05,852.792 1722.05,851.549 1723.05,850.331 1724.06,849.138 1725.06,847.97 1726.07,846.825 1727.07,845.705 1728.08,844.608 1729.08,843.534 1730.08,842.483 \n",
       "  1731.09,841.455 1732.09,840.45 1733.1,839.467 1734.1,838.505 1735.11,837.566 1736.11,836.647 1737.12,835.75 1738.12,834.874 1739.12,834.019 1740.13,833.184 \n",
       "  1741.13,832.369 1742.14,831.575 1743.14,830.8 1744.15,830.045 1745.15,829.309 1746.15,828.592 1747.16,827.894 1748.16,827.215 1749.17,826.554 1750.17,825.912 \n",
       "  1751.18,825.288 1752.18,824.682 1753.18,824.094 1754.19,823.524 1755.19,822.971 1756.2,822.436 1757.2,821.917 1758.21,821.416 1759.21,820.932 1760.22,820.464 \n",
       "  1761.22,820.013 1762.22,819.579 1763.23,819.161 1764.23,818.759 1765.24,818.373 1766.24,818.003 1767.25,817.65 1768.25,817.312 1769.25,816.989 1770.26,816.683 \n",
       "  1771.26,816.392 1772.27,816.116 1773.27,815.856 1774.28,815.611 1775.28,815.381 1776.29,815.166 1777.29,814.966 1778.29,814.782 1779.3,814.612 1780.3,814.457 \n",
       "  1781.31,814.318 1782.31,814.192 1783.32,814.082 1784.32,813.987 1785.32,813.906 1786.33,813.84 1787.33,813.788 1788.34,813.752 1789.34,813.729 1790.35,813.722 \n",
       "  1791.35,813.729 1792.35,813.751 1793.36,813.788 1794.36,813.839 1795.37,813.905 1796.37,813.985 1797.38,814.08 1798.38,814.19 1799.39,814.315 1800.39,814.455 \n",
       "  1801.39,814.609 1802.4,814.779 1803.4,814.963 1804.41,815.162 1805.41,815.377 1806.42,815.606 1807.42,815.851 1808.42,816.111 1809.43,816.387 1810.43,816.678 \n",
       "  1811.44,816.984 1812.44,817.306 1813.45,817.644 1814.45,817.997 1815.46,818.367 1816.46,818.752 1817.46,819.154 1818.47,819.572 1819.47,820.006 1820.48,820.456 \n",
       "  1821.48,820.924 1822.49,821.408 1823.49,821.909 1824.49,822.427 1825.5,822.962 1826.5,823.515 1827.51,824.085 1828.51,824.673 1829.52,825.279 1830.52,825.902 \n",
       "  1831.52,826.544 1832.53,827.205 1833.53,827.883 1834.54,828.581 1835.54,829.298 1836.55,830.033 1837.55,830.789 1838.56,831.563 1839.56,832.358 1840.56,833.172 \n",
       "  1841.57,834.007 1842.57,834.862 1843.58,835.738 1844.58,836.635 1845.59,837.553 1846.59,838.493 1847.59,839.454 1848.6,840.437 1849.6,841.443 1850.61,842.47 \n",
       "  1851.61,843.521 1852.62,844.595 1853.62,845.692 1854.63,846.812 1855.63,847.957 1856.63,849.125 1857.64,850.319 1858.64,851.537 1859.65,852.78 1860.65,854.048 \n",
       "  1861.66,855.342 1862.66,856.662 1863.66,858.009 1864.67,859.382 1865.67,860.782 1866.68,862.21 1867.68,863.665 1868.69,865.148 1869.69,866.66 1870.69,868.2 \n",
       "  1871.7,869.77 1872.7,871.368 1873.71,872.997 1874.71,874.656 1875.72,876.345 1876.72,878.065 1877.73,879.816 1878.73,881.599 1879.73,883.414 1880.74,885.261 \n",
       "  1881.74,887.14 1882.75,889.053 1883.75,890.999 1884.76,892.979 1885.76,894.993 1886.76,897.042 1887.77,899.125 1888.77,901.244 1889.78,903.399 1890.78,905.589 \n",
       "  1891.79,907.816 1892.79,910.079 1893.79,912.379 1894.8,914.717 1895.8,917.093 1896.81,919.506 1897.81,921.959 1898.82,924.45 1899.82,926.98 1900.83,929.549 \n",
       "  1901.83,932.158 1902.83,934.807 1903.84,937.497 1904.84,940.227 1905.85,942.998 1906.85,945.811 1907.86,948.664 1908.86,951.56 1909.86,954.497 1910.87,957.477 \n",
       "  1911.87,960.499 1912.88,963.564 1913.88,966.671 1914.89,969.822 1915.89,973.015 1916.9,976.252 1917.9,979.532 1918.9,982.856 1919.91,986.224 1920.91,989.635 \n",
       "  1921.92,993.089 1922.92,996.588 1923.93,1000.13 1924.93,1003.72 1925.93,1007.35 1926.94,1011.02 1927.94,1014.74 1928.95,1018.5 1929.95,1022.3 1930.96,1026.15 \n",
       "  1931.96,1030.04 1932.96,1033.97 1933.97,1037.95 1934.97,1041.96 1935.98,1046.02 1936.98,1050.12 1937.99,1054.27 1938.99,1058.45 1940,1062.67 1941,1066.93 \n",
       "  1942,1071.24 1943.01,1075.58 1944.01,1079.96 1945.02,1084.37 1946.02,1088.83 1947.03,1093.32 1948.03,1097.84 1949.03,1102.4 1950.04,1106.99 1951.04,1111.62 \n",
       "  1952.05,1116.28 1953.05,1120.96 1954.06,1125.68 1955.06,1130.43 1956.07,1135.2 1957.07,1140 1958.07,1144.83 1959.08,1149.68 1960.08,1154.56 1961.09,1159.45 \n",
       "  1962.09,1164.37 1963.1,1169.3 1964.1,1174.25 1965.1,1179.22 1966.11,1184.2 1967.11,1189.19 1968.12,1194.19 1969.12,1199.21 1970.13,1204.23 1971.13,1209.25 \n",
       "  1972.13,1214.28 1973.14,1219.31 1974.14,1224.34 1975.15,1229.37 1976.15,1234.4 1977.16,1239.42 1978.16,1244.43 1979.17,1249.43 1980.17,1254.42 1981.17,1259.39 \n",
       "  1982.18,1264.35 1983.18,1269.29 1984.19,1274.2 1985.19,1279.1 1986.2,1283.96 1987.2,1288.8 1988.2,1293.61 1989.21,1298.38 1990.21,1303.12 1991.22,1307.82 \n",
       "  1992.22,1312.48 1993.23,1317.1 1994.23,1321.67 1995.23,1326.2 1996.24,1330.67 1997.24,1335.09 1998.25,1339.46 1999.25,1343.76 2000.26,1348.01 2001.26,1352.19 \n",
       "  2002.27,1356.31 2003.27,1360.36 2004.27,1364.34 2005.28,1368.25 2006.28,1372.08 2007.29,1375.84 2008.29,1379.52 2009.3,1383.11 2010.3,1386.62 2011.3,1390.04 \n",
       "  2012.31,1393.37 2013.31,1396.62 2014.32,1399.77 2015.32,1402.82 2016.33,1405.78 2017.33,1408.63 2018.34,1411.39 2019.34,1414.04 2020.34,1416.59 2021.35,1419.03 \n",
       "  2022.35,1421.36 2023.36,1423.58 2024.36,1425.69 2025.37,1427.69 2026.37,1429.58 2027.37,1431.34 2028.38,1432.99 2029.38,1434.52 2030.39,1435.94 2031.39,1437.23 \n",
       "  2032.4,1438.4 2033.4,1439.45 2034.4,1440.37 2035.41,1441.18 2036.41,1441.85 2037.42,1442.41 2038.42,1442.83 2039.43,1443.14 2040.43,1443.31 2041.44,1443.36 \n",
       "  2042.44,1443.29 2043.44,1443.09 2044.45,1442.76 2045.45,1442.31 2046.46,1441.73 2047.46,1441.03 2048.47,1440.2 2049.47,1439.25 2050.47,1438.17 2051.48,1436.98 \n",
       "  2052.48,1435.66 2053.49,1434.22 2054.49,1432.66 2055.5,1430.99 2056.5,1429.2 2057.51,1427.29 2058.51,1425.26 2059.51,1423.12 2060.52,1420.87 2061.52,1418.52 \n",
       "  2062.53,1416.05 2063.53,1413.47 2064.54,1410.79 2065.54,1408.01 2066.54,1405.12 2067.55,1402.14 2068.55,1399.05 2069.56,1395.88 2070.56,1392.6 2071.57,1389.24 \n",
       "  2072.57,1385.79 2073.57,1382.25 2074.58,1378.62 2075.58,1374.92 2076.59,1371.13 2077.59,1367.27 2078.6,1363.33 2079.6,1359.31 2080.61,1355.23 2081.61,1351.08 \n",
       "  2082.61,1346.86 2083.62,1342.58 2084.62,1338.24 2085.63,1333.84 2086.63,1329.38 2087.64,1324.87 2088.64,1320.31 2089.64,1315.7 2090.65,1311.05 2091.65,1306.35 \n",
       "  2092.66,1301.61 2093.66,1296.84 2094.67,1292.02 2095.67,1287.18 2096.68,1282.3 2097.68,1277.39 2098.68,1272.46 2099.69,1267.5 2100.69,1262.52 2101.7,1257.53 \n",
       "  2102.7,1252.51 2103.71,1247.48 2104.71,1242.44 2105.71,1237.38 2106.72,1232.32 2107.72,1227.25 2108.73,1222.18 2109.73,1217.1 2110.74,1212.02 2111.74,1206.95 \n",
       "  2112.74,1201.87 2113.75,1196.81 2114.75,1191.75 2115.76,1186.69 2116.76,1181.65 2117.77,1176.62 2118.77,1171.61 2119.78,1166.6 2120.78,1161.62 2121.78,1156.65 \n",
       "  2122.79,1151.71 2123.79,1146.78 2124.8,1141.88 2125.8,1137 2126.81,1132.14 2127.81,1127.31 2128.81,1122.51 2129.82,1117.74 2130.82,1112.99 2131.83,1108.28 \n",
       "  2132.83,1103.59 2133.84,1098.94 2134.84,1094.32 2135.84,1089.74 2136.85,1085.19 2137.85,1080.67 2138.86,1076.19 2139.86,1071.75 2140.87,1067.35 2141.87,1062.98 \n",
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       "  997.909,186.682 998.913,182.582 999.917,178.551 1000.92,174.59 1001.93,170.702 1002.93,166.889 1003.93,163.155 1004.94,159.5 1005.94,155.927 1006.95,152.439 \n",
       "  1007.95,149.038 1008.96,145.726 1009.96,142.505 1010.97,139.378 1011.97,136.345 1012.97,133.41 1013.98,130.574 1014.98,127.84 1015.99,125.208 1016.99,122.681 \n",
       "  1018,120.26 1019,117.948 1020,115.745 1021.01,113.654 1022.01,111.675 1023.02,109.81 1024.02,108.061 1025.03,106.428 1026.03,104.913 1027.03,103.516 \n",
       "  1028.04,102.24 1029.04,101.084 1030.05,100.049 1031.05,99.1366 1032.06,98.3471 1033.06,97.681 1034.07,97.1387 1035.07,96.7206 1036.07,96.427 1037.08,96.2581 \n",
       "  1038.08,96.2141 1039.09,96.2949 1040.09,96.5004 1041.1,96.8306 1042.1,97.2851 1043.1,97.8635 1044.11,98.5656 1045.11,99.3906 1046.12,100.338 1047.12,101.407 \n",
       "  1048.13,102.598 1049.13,103.908 1050.14,105.337 1051.14,106.885 1052.14,108.549 1053.15,110.33 1054.15,112.224 1055.16,114.232 1056.16,116.352 1057.17,118.582 \n",
       "  1058.17,120.921 1059.17,123.367 1060.18,125.918 1061.18,128.573 1062.19,131.33 1063.19,134.186 1064.2,137.141 1065.2,140.191 1066.2,143.336 1067.21,146.572 \n",
       "  1068.21,149.899 1069.22,153.313 1070.22,156.812 1071.23,160.394 1072.23,164.057 1073.24,167.799 1074.24,171.617 1075.24,175.509 1076.25,179.472 1077.25,183.505 \n",
       "  1078.26,187.604 1079.26,191.767 1080.27,195.992 1081.27,200.276 1082.27,204.617 1083.28,209.012 1084.28,213.459 1085.29,217.956 1086.29,222.499 1087.3,227.087 \n",
       "  1088.3,231.717 1089.31,236.386 1090.31,241.092 1091.31,245.834 1092.32,250.607 1093.32,255.41 1094.33,260.241 1095.33,265.097 1096.34,269.976 1097.34,274.876 \n",
       "  1098.34,279.793 1099.35,284.728 1100.35,289.676 1101.36,294.635 1102.36,299.605 1103.37,304.582 1104.37,309.564 1105.37,314.55 1106.38,319.538 1107.38,324.525 \n",
       "  1108.39,329.51 1109.39,334.491 1110.4,339.465 1111.4,344.432 1112.41,349.39 1113.41,354.337 1114.41,359.27 1115.42,364.19 1116.42,369.093 1117.43,373.979 \n",
       "  1118.43,378.846 1119.44,383.693 1120.44,388.518 1121.44,393.321 1122.45,398.099 1123.45,402.852 1124.46,407.578 1125.46,412.277 1126.47,416.946 1127.47,421.586 \n",
       "  1128.48,426.195 1129.48,430.772 1130.48,435.317 1131.49,439.827 1132.49,444.304 1133.5,448.745 1134.5,453.15 1135.51,457.519 1136.51,461.85 1137.51,466.144 \n",
       "  1138.52,470.398 1139.52,474.614 1140.53,478.79 1141.53,482.926 1142.54,487.022 1143.54,491.077 1144.54,495.09 1145.55,499.062 1146.55,502.992 1147.56,506.88 \n",
       "  1148.56,510.725 1149.57,514.528 1150.57,518.288 1151.58,522.005 1152.58,525.678 1153.58,529.309 1154.59,532.896 1155.59,536.44 1156.6,539.94 1157.6,543.397 \n",
       "  1158.61,546.811 1159.61,550.181 1160.61,553.508 1161.62,556.792 1162.62,560.033 1163.63,563.231 1164.63,566.386 1165.64,569.498 1166.64,572.567 1167.64,575.594 \n",
       "  1168.65,578.579 1169.65,581.522 1170.66,584.423 1171.66,587.283 1172.67,590.101 1173.67,592.878 1174.68,595.615 1175.68,598.311 1176.68,600.967 1177.69,603.582 \n",
       "  1178.69,606.159 1179.7,608.695 1180.7,611.193 1181.71,613.652 1182.71,616.073 1183.71,618.456 1184.72,620.801 1185.72,623.109 1186.73,625.38 1187.73,627.614 \n",
       "  1188.74,629.811 1189.74,631.973 1190.75,634.1 1191.75,636.191 1192.75,638.247 1193.76,640.268 1194.76,642.256 1195.77,644.21 1196.77,646.13 1197.78,648.017 \n",
       "  1198.78,649.872 1199.78,651.694 1200.79,653.484 1201.79,655.243 1202.8,656.971 1203.8,658.668 1204.81,660.334 1205.81,661.97 1206.81,663.576 1207.82,665.153 \n",
       "  1208.82,666.701 1209.83,668.22 1210.83,669.71 1211.84,671.173 1212.84,672.608 1213.85,674.015 1214.85,675.396 1215.85,676.749 1216.86,678.077 1217.86,679.378 \n",
       "  1218.87,680.653 1219.87,681.903 1220.88,683.128 1221.88,684.329 1222.88,685.504 1223.89,686.656 1224.89,687.783 1225.9,688.887 1226.9,689.968 1227.91,691.025 \n",
       "  1228.91,692.06 1229.92,693.072 1230.92,694.062 1231.92,695.03 1232.93,695.976 1233.93,696.901 1234.94,697.804 1235.94,698.687 1236.95,699.549 1237.95,700.39 \n",
       "  1238.95,701.211 1239.96,702.012 1240.96,702.794 1241.97,703.555 1242.97,704.297 1243.98,705.021 1244.98,705.725 1245.98,706.41 1246.99,707.077 1247.99,707.725 \n",
       "  1249,708.355 1250,708.967 1251.01,709.561 1252.01,710.138 1253.02,710.697 1254.02,711.239 1255.02,711.763 1256.03,712.271 1257.03,712.761 1258.04,713.235 \n",
       "  1259.04,713.692 1260.05,714.133 1261.05,714.557 1262.05,714.965 1263.06,715.357 1264.06,715.733 1265.07,716.093 1266.07,716.437 1267.08,716.765 1268.08,717.078 \n",
       "  1269.08,717.376 1270.09,717.658 1271.09,717.925 1272.1,718.176 1273.1,718.412 1274.11,718.633 1275.11,718.84 1276.12,719.031 1277.12,719.207 1278.12,719.368 \n",
       "  1279.13,719.515 1280.13,719.647 1281.14,719.764 1282.14,719.866 1283.15,719.954 1284.15,720.027 1285.15,720.085 1286.16,720.129 1287.16,720.158 1288.17,720.172 \n",
       "  1289.17,720.172 1290.18,720.158 1291.18,720.129 1292.19,720.085 1293.19,720.027 1294.19,719.954 1295.2,719.866 1296.2,719.764 1297.21,719.647 1298.21,719.515 \n",
       "  1299.22,719.368 1300.22,719.207 1301.22,719.031 1302.23,718.84 1303.23,718.633 1304.24,718.412 1305.24,718.176 1306.25,717.925 1307.25,717.658 1308.25,717.376 \n",
       "  1309.26,717.078 1310.26,716.765 1311.27,716.437 1312.27,716.093 1313.28,715.733 1314.28,715.357 1315.29,714.965 1316.29,714.557 1317.29,714.133 1318.3,713.692 \n",
       "  1319.3,713.235 1320.31,712.761 1321.31,712.271 1322.32,711.763 1323.32,711.239 1324.32,710.697 1325.33,710.138 1326.33,709.561 1327.34,708.967 1328.34,708.355 \n",
       "  1329.35,707.725 1330.35,707.077 1331.36,706.41 1332.36,705.725 1333.36,705.021 1334.37,704.297 1335.37,703.555 1336.38,702.794 1337.38,702.012 1338.39,701.211 \n",
       "  1339.39,700.39 1340.39,699.549 1341.4,698.687 1342.4,697.804 1343.41,696.901 1344.41,695.976 1345.42,695.03 1346.42,694.062 1347.42,693.072 1348.43,692.06 \n",
       "  1349.43,691.025 1350.44,689.968 1351.44,688.887 1352.45,687.783 1353.45,686.656 1354.46,685.504 1355.46,684.329 1356.46,683.128 1357.47,681.903 1358.47,680.653 \n",
       "  1359.48,679.378 1360.48,678.077 1361.49,676.749 1362.49,675.396 1363.49,674.015 1364.5,672.608 1365.5,671.173 1366.51,669.71 1367.51,668.22 1368.52,666.701 \n",
       "  1369.52,665.153 1370.53,663.576 1371.53,661.97 1372.53,660.334 1373.54,658.668 1374.54,656.971 1375.55,655.243 1376.55,653.484 1377.56,651.694 1378.56,649.872 \n",
       "  1379.56,648.017 1380.57,646.13 1381.57,644.21 1382.58,642.256 1383.58,640.268 1384.59,638.247 1385.59,636.191 1386.59,634.1 1387.6,631.973 1388.6,629.811 \n",
       "  1389.61,627.614 1390.61,625.38 1391.62,623.109 1392.62,620.801 1393.63,618.456 1394.63,616.073 1395.63,613.652 1396.64,611.193 1397.64,608.695 1398.65,606.159 \n",
       "  1399.65,603.582 1400.66,600.967 1401.66,598.311 1402.66,595.615 1403.67,592.878 1404.67,590.101 1405.68,587.283 1406.68,584.423 1407.69,581.522 1408.69,578.579 \n",
       "  1409.69,575.594 1410.7,572.567 1411.7,569.498 1412.71,566.386 1413.71,563.231 1414.72,560.033 1415.72,556.792 1416.73,553.508 1417.73,550.181 1418.73,546.811 \n",
       "  1419.74,543.397 1420.74,539.94 1421.75,536.44 1422.75,532.896 1423.76,529.309 1424.76,525.678 1425.76,522.005 1426.77,518.288 1427.77,514.528 1428.78,510.725 \n",
       "  1429.78,506.88 1430.79,502.992 1431.79,499.062 1432.8,495.09 1433.8,491.077 1434.8,487.022 1435.81,482.926 1436.81,478.79 1437.82,474.614 1438.82,470.398 \n",
       "  1439.83,466.144 1440.83,461.85 1441.83,457.519 1442.84,453.15 1443.84,448.745 1444.85,444.304 1445.85,439.827 1446.86,435.317 1447.86,430.772 1448.86,426.195 \n",
       "  1449.87,421.586 1450.87,416.946 1451.88,412.277 1452.88,407.578 1453.89,402.852 1454.89,398.099 1455.9,393.321 1456.9,388.518 1457.9,383.693 1458.91,378.846 \n",
       "  1459.91,373.979 1460.92,369.093 1461.92,364.19 1462.93,359.27 1463.93,354.337 1464.93,349.39 1465.94,344.432 1466.94,339.465 1467.95,334.491 1468.95,329.51 \n",
       "  1469.96,324.525 1470.96,319.538 1471.97,314.55 1472.97,309.564 1473.97,304.582 1474.98,299.605 1475.98,294.635 1476.99,289.676 1477.99,284.728 1479,279.793 \n",
       "  1480,274.876 1481,269.976 1482.01,265.097 1483.01,260.241 1484.02,255.41 1485.02,250.607 1486.03,245.834 1487.03,241.092 1488.03,236.386 1489.04,231.717 \n",
       "  1490.04,227.087 1491.05,222.499 1492.05,217.956 1493.06,213.459 1494.06,209.012 1495.07,204.617 1496.07,200.276 1497.07,195.992 1498.08,191.767 1499.08,187.604 \n",
       "  1500.09,183.505 1501.09,179.472 1502.1,175.509 1503.1,171.617 1504.1,167.799 1505.11,164.057 1506.11,160.394 1507.12,156.812 1508.12,153.313 1509.13,149.899 \n",
       "  1510.13,146.572 1511.13,143.336 1512.14,140.191 1513.14,137.141 1514.15,134.186 1515.15,131.33 1516.16,128.573 1517.16,125.918 1518.17,123.367 1519.17,120.921 \n",
       "  1520.17,118.582 1521.18,116.352 1522.18,114.232 1523.19,112.224 1524.19,110.33 1525.2,108.549 1526.2,106.885 1527.2,105.337 1528.21,103.908 1529.21,102.598 \n",
       "  1530.22,101.407 1531.22,100.338 1532.23,99.3907 1533.23,98.5656 1534.24,97.8635 1535.24,97.2851 1536.24,96.8306 1537.25,96.5004 1538.25,96.2949 1539.26,96.2141 \n",
       "  1540.26,96.2582 1541.27,96.427 1542.27,96.7206 1543.27,97.1387 1544.28,97.681 1545.28,98.3471 1546.29,99.1367 1547.29,100.049 1548.3,101.084 1549.3,102.24 \n",
       "  1550.3,103.516 1551.31,104.913 1552.31,106.428 1553.32,108.061 1554.32,109.81 1555.33,111.675 1556.33,113.654 1557.34,115.745 1558.34,117.948 1559.34,120.26 \n",
       "  1560.35,122.681 1561.35,125.208 1562.36,127.84 1563.36,130.574 1564.37,133.41 1565.37,136.345 1566.37,139.378 1567.38,142.505 1568.38,145.726 1569.39,149.038 \n",
       "  1570.39,152.439 1571.4,155.927 1572.4,159.5 1573.41,163.155 1574.41,166.889 1575.41,170.702 1576.42,174.59 1577.42,178.551 1578.43,182.582 1579.43,186.682 \n",
       "  1580.44,190.848 1581.44,195.077 1582.44,199.366 1583.45,203.714 1584.45,208.118 1585.46,212.576 1586.46,217.084 1587.47,221.641 1588.47,226.245 1589.47,230.891 \n",
       "  1590.48,235.579 1591.48,240.306 1592.49,245.069 1593.49,249.865 1594.5,254.694 1595.5,259.551 1596.51,264.436 1597.51,269.344 1598.51,274.275 1599.52,279.226 \n",
       "  1600.52,284.195 1601.53,289.179 1602.53,294.176 1603.54,299.185 1604.54,304.202 1605.54,309.227 1606.55,314.256 1607.55,319.289 1608.56,324.323 1609.56,329.355 \n",
       "  1610.57,334.385 1611.57,339.411 1612.58,344.43 1613.58,349.441 1614.58,354.442 1615.59,359.432 1616.59,364.409 1617.6,369.371 1618.6,374.317 1619.61,379.245 \n",
       "  1620.61,384.154 1621.61,389.043 1622.62,393.911 1623.62,398.755 1624.63,403.575 1625.63,408.37 1626.64,413.138 1627.64,417.879 1628.64,422.59 1629.65,427.272 \n",
       "  1630.65,431.924 1631.66,436.543 1632.66,441.131 1633.67,445.685 1634.67,450.204 1635.68,454.689 1636.68,459.139 1637.68,463.552 1638.69,467.928 1639.69,472.267 \n",
       "  1640.7,476.568 1641.7,480.83 1642.71,485.053 1643.71,489.237 1644.71,493.381 1645.72,497.485 1646.72,501.548 1647.73,505.571 1648.73,509.552 1649.74,513.492 \n",
       "  1650.74,517.39 1651.74,521.247 1652.75,525.062 1653.75,528.834 1654.76,532.565 1655.76,536.253 1656.77,539.9 1657.77,543.504 1658.78,547.065 1659.78,550.585 \n",
       "  1660.78,554.062 1661.79,557.498 1662.79,560.891 1663.8,564.243 1664.8,567.552 1665.81,570.821 1666.81,574.047 1667.81,577.233 1668.82,580.378 1669.82,583.481 \n",
       "  1670.83,586.545 1671.83,589.568 1672.84,592.55 1673.84,595.493 1674.85,598.397 1675.85,601.261 1676.85,604.087 1677.86,606.873 1678.86,609.622 1679.87,612.333 \n",
       "  1680.87,615.006 1681.88,617.641 1682.88,620.24 1683.88,622.803 1684.89,625.329 1685.89,627.819 1686.9,630.275 1687.9,632.695 1688.91,635.08 1689.91,637.432 \n",
       "  1690.91,639.749 1691.92,642.034 1692.92,644.285 1693.93,646.503 1694.93,648.69 1695.94,650.845 1696.94,652.968 1697.95,655.061 1698.95,657.123 1699.95,659.155 \n",
       "  1700.96,661.157 1701.96,663.13 1702.97,665.074 1703.97,666.99 1704.98,668.878 1705.98,670.738 1706.98,672.572 1707.99,674.378 1708.99,676.159 1710,677.913 \n",
       "  1711,679.642 1712.01,681.346 1713.01,683.025 1714.02,684.68 1715.02,686.311 1716.02,687.919 1717.03,689.504 1718.03,691.066 1719.04,692.606 1720.04,694.124 \n",
       "  1721.05,695.621 1722.05,697.097 1723.05,698.552 1724.06,699.987 1725.06,701.402 1726.07,702.797 1727.07,704.174 1728.08,705.531 1729.08,706.871 1730.08,708.192 \n",
       "  1731.09,709.496 1732.09,710.782 1733.1,712.051 1734.1,713.304 1735.11,714.541 1736.11,715.762 1737.12,716.967 1738.12,718.157 1739.12,719.333 1740.13,720.494 \n",
       "  1741.13,721.64 1742.14,722.773 1743.14,723.893 1744.15,724.999 1745.15,726.093 1746.15,727.174 1747.16,728.243 1748.16,729.3 1749.17,730.345 1750.17,731.379 \n",
       "  1751.18,732.402 1752.18,733.415 1753.18,734.417 1754.19,735.41 1755.19,736.392 1756.2,737.365 1757.2,738.33 1758.21,739.285 1759.21,740.231 1760.22,741.17 \n",
       "  1761.22,742.1 1762.22,743.023 1763.23,743.939 1764.23,744.847 1765.24,745.748 1766.24,746.643 1767.25,747.532 1768.25,748.414 1769.25,749.291 1770.26,750.163 \n",
       "  1771.26,751.029 1772.27,751.89 1773.27,752.747 1774.28,753.599 1775.28,754.447 1776.29,755.291 1777.29,756.132 1778.29,756.969 1779.3,757.803 1780.3,758.635 \n",
       "  1781.31,759.463 1782.31,760.29 1783.32,761.114 1784.32,761.937 1785.32,762.758 1786.33,763.578 1787.33,764.397 1788.34,765.215 1789.34,766.033 1790.35,766.85 \n",
       "  1791.35,767.667 1792.35,768.485 1793.36,769.303 1794.36,770.122 1795.37,770.941 1796.37,771.763 1797.38,772.585 1798.38,773.41 1799.39,774.236 1800.39,775.065 \n",
       "  1801.39,775.896 1802.4,776.731 1803.4,777.568 1804.41,778.409 1805.41,779.253 1806.42,780.101 1807.42,780.953 1808.42,781.81 1809.43,782.671 1810.43,783.538 \n",
       "  1811.44,784.409 1812.44,785.286 1813.45,786.169 1814.45,787.057 1815.46,787.952 1816.46,788.854 1817.46,789.762 1818.47,790.678 1819.47,791.6 1820.48,792.531 \n",
       "  1821.48,793.47 1822.49,794.416 1823.49,795.372 1824.49,796.336 1825.5,797.309 1826.5,798.292 1827.51,799.284 1828.51,800.287 1829.52,801.3 1830.52,802.323 \n",
       "  1831.52,803.357 1832.53,804.403 1833.53,805.46 1834.54,806.529 1835.54,807.61 1836.55,808.704 1837.55,809.811 1838.56,810.93 1839.56,812.063 1840.56,813.21 \n",
       "  1841.57,814.372 1842.57,815.547 1843.58,816.738 1844.58,817.943 1845.59,819.165 1846.59,820.402 1847.59,821.655 1848.6,822.925 1849.6,824.211 1850.61,825.515 \n",
       "  1851.61,826.837 1852.62,828.177 1853.62,829.535 1854.63,830.912 1855.63,832.308 1856.63,833.723 1857.64,835.159 1858.64,836.614 1859.65,838.091 1860.65,839.588 \n",
       "  1861.66,841.107 1862.66,842.648 1863.66,844.211 1864.67,845.796 1865.67,847.405 1866.68,849.037 1867.68,850.693 1868.69,852.373 1869.69,854.078 1870.69,855.808 \n",
       "  1871.7,857.564 1872.7,859.345 1873.71,861.153 1874.71,862.987 1875.72,864.849 1876.72,866.738 1877.73,868.656 1878.73,870.601 1879.73,872.576 1880.74,874.58 \n",
       "  1881.74,876.614 1882.75,878.678 1883.75,880.772 1884.76,882.897 1885.76,885.054 1886.76,887.243 1887.77,889.464 1888.77,891.718 1889.78,894.004 1890.78,896.324 \n",
       "  1891.79,898.679 1892.79,901.067 1893.79,903.49 1894.8,905.948 1895.8,908.442 1896.81,910.972 1897.81,913.538 1898.82,916.141 1899.82,918.78 1900.83,921.457 \n",
       "  1901.83,924.172 1902.83,926.925 1903.84,929.716 1904.84,932.547 1905.85,935.416 1906.85,938.325 1907.86,941.273 1908.86,944.262 1909.86,947.29 1910.87,950.36 \n",
       "  1911.87,953.47 1912.88,956.621 1913.88,959.814 1914.89,963.048 1915.89,966.324 1916.9,969.641 1917.9,973.001 1918.9,976.403 1919.91,979.847 1920.91,983.333 \n",
       "  1921.92,986.862 1922.92,990.434 1923.93,994.048 1924.93,997.705 1925.93,1001.4 1926.94,1005.15 1927.94,1008.93 1928.95,1012.76 1929.95,1016.63 1930.96,1020.54 \n",
       "  1931.96,1024.49 1932.96,1028.49 1933.97,1032.52 1934.97,1036.6 1935.98,1040.72 1936.98,1044.88 1937.99,1049.08 1938.99,1053.32 1940,1057.6 1941,1061.92 \n",
       "  1942,1066.28 1943.01,1070.68 1944.01,1075.11 1945.02,1079.58 1946.02,1084.09 1947.03,1088.63 1948.03,1093.21 1949.03,1097.82 1950.04,1102.46 1951.04,1107.14 \n",
       "  1952.05,1111.85 1953.05,1116.59 1954.06,1121.35 1955.06,1126.15 1956.07,1130.97 1957.07,1135.82 1958.07,1140.7 1959.08,1145.6 1960.08,1150.52 1961.09,1155.46 \n",
       "  1962.09,1160.42 1963.1,1165.41 1964.1,1170.4 1965.1,1175.42 1966.11,1180.44 1967.11,1185.48 1968.12,1190.53 1969.12,1195.59 1970.13,1200.66 1971.13,1205.73 \n",
       "  1972.13,1210.81 1973.14,1215.89 1974.14,1220.97 1975.15,1226.04 1976.15,1231.11 1977.16,1236.18 1978.16,1241.24 1979.17,1246.28 1980.17,1251.32 1981.17,1256.34 \n",
       "  1982.18,1261.34 1983.18,1266.33 1984.19,1271.29 1985.19,1276.23 1986.2,1281.15 1987.2,1286.03 1988.2,1290.89 1989.21,1295.71 1990.21,1300.5 1991.22,1305.25 \n",
       "  1992.22,1309.95 1993.23,1314.62 1994.23,1319.24 1995.23,1323.81 1996.24,1328.34 1997.24,1332.81 1998.25,1337.22 1999.25,1341.58 2000.26,1345.88 2001.26,1350.11 \n",
       "  2002.27,1354.28 2003.27,1358.38 2004.27,1362.41 2005.28,1366.37 2006.28,1370.26 2007.29,1374.06 2008.29,1377.79 2009.3,1381.44 2010.3,1385 2011.3,1388.47 \n",
       "  2012.31,1391.86 2013.31,1395.16 2014.32,1398.36 2015.32,1401.47 2016.33,1404.48 2017.33,1407.39 2018.34,1410.2 2019.34,1412.9 2020.34,1415.51 2021.35,1418 \n",
       "  2022.35,1420.39 2023.36,1422.67 2024.36,1424.83 2025.37,1426.89 2026.37,1428.82 2027.37,1430.65 2028.38,1432.35 2029.38,1433.94 2030.39,1435.41 2031.39,1436.76 \n",
       "  2032.4,1437.98 2033.4,1439.09 2034.4,1440.07 2035.41,1440.93 2036.41,1441.66 2037.42,1442.27 2038.42,1442.76 2039.43,1443.11 2040.43,1443.35 2041.44,1443.45 \n",
       "  2042.44,1443.43 2043.44,1443.29 2044.45,1443.02 2045.45,1442.62 2046.46,1442.1 2047.46,1441.45 2048.47,1440.68 2049.47,1439.79 2050.47,1438.77 2051.48,1437.63 \n",
       "  2052.48,1436.37 2053.49,1434.99 2054.49,1433.48 2055.5,1431.86 2056.5,1430.12 2057.51,1428.27 2058.51,1426.3 2059.51,1424.22 2060.52,1422.02 2061.52,1419.72 \n",
       "  2062.53,1417.3 2063.53,1414.78 2064.54,1412.15 2065.54,1409.42 2066.54,1406.59 2067.55,1403.66 2068.55,1400.63 2069.56,1397.5 2070.56,1394.28 2071.57,1390.97 \n",
       "  2072.57,1387.57 2073.57,1384.08 2074.58,1380.51 2075.58,1376.85 2076.59,1373.12 2077.59,1369.3 2078.6,1365.41 2079.6,1361.45 2080.61,1357.41 2081.61,1353.31 \n",
       "  2082.61,1349.14 2083.62,1344.91 2084.62,1340.62 2085.63,1336.27 2086.63,1331.86 2087.64,1327.4 2088.64,1322.88 2089.64,1318.32 2090.65,1313.72 2091.65,1309.07 \n",
       "  2092.66,1304.37 2093.66,1299.64 2094.67,1294.88 2095.67,1290.08 2096.68,1285.24 2097.68,1280.38 2098.68,1275.5 2099.69,1270.58 2100.69,1265.65 2101.7,1260.7 \n",
       "  2102.7,1255.73 2103.71,1250.74 2104.71,1245.74 2105.71,1240.73 2106.72,1235.72 2107.72,1230.69 2108.73,1225.66 2109.73,1220.63 2110.74,1215.6 2111.74,1210.57 \n",
       "  2112.74,1205.54 2113.75,1200.51 2114.75,1195.5 2115.76,1190.49 2116.76,1185.49 2117.77,1180.51 2118.77,1175.54 2119.78,1170.58 2120.78,1165.64 2121.78,1160.72 \n",
       "  2122.79,1155.82 2123.79,1150.94 2124.8,1146.09 2125.8,1141.25 2126.81,1136.44 2127.81,1131.66 2128.81,1126.91 2129.82,1122.18 2130.82,1117.48 2131.83,1112.82 \n",
       "  2132.83,1108.18 2133.84,1103.58 2134.84,1099.01 2135.84,1094.48 2136.85,1089.98 2137.85,1085.51 2138.86,1081.09 2139.86,1076.7 2140.87,1072.35 2141.87,1068.03 \n",
       "  2142.88,1063.76 2143.88,1059.53 2144.88,1055.33 2145.89,1051.18 2146.89,1047.07 2147.9,1043 2148.9,1038.97 2149.91,1034.98 2150.91,1031.04 2151.91,1027.14 \n",
       "  2152.92,1023.28 2153.92,1019.46 2154.93,1015.69 2155.93,1011.96 2156.94,1008.27 2157.94,1004.63 2158.95,1001.03 2159.95,997.481 2160.95,993.97 2161.96,990.503 \n",
       "  2162.96,987.081 2163.97,983.701 2164.97,980.366 2165.98,977.074 2166.98,973.825 2167.98,970.62 2168.99,967.458 2169.99,964.339 2171,961.262 2172,958.229 \n",
       "  2173.01,955.238 2174.01,952.289 2175.01,949.382 2176.02,946.517 2177.02,943.693 2178.03,940.911 2179.03,938.17 2180.04,935.469 2181.04,932.809 2182.05,930.189 \n",
       "  2183.05,927.609 2184.05,925.068 2185.06,922.566 2186.06,920.103 2187.07,917.679 2188.07,915.293 2189.08,912.945 2190.08,910.634 2191.08,908.361 2192.09,906.124 \n",
       "  2193.09,903.924 2194.1,901.759 2195.1,899.631 2196.11,897.538 2197.11,895.479 2198.12,893.456 2199.12,891.466 2200.12,889.511 2201.13,887.588 2202.13,885.7 \n",
       "  2203.14,883.843 2204.14,882.019 2205.15,880.228 2206.15,878.468 2207.15,876.739 2208.16,875.041 2209.16,873.373 2210.17,871.736 2211.17,870.129 2212.18,868.551 \n",
       "  2213.18,867.002 2214.18,865.482 2215.19,863.991 2216.19,862.528 2217.2,861.092 2218.2,859.684 2219.21,858.303 2220.21,856.948 2221.22,855.62 2222.22,854.318 \n",
       "  2223.22,853.042 2224.23,851.792 2225.23,850.566 2226.24,849.366 2227.24,848.19 2228.25,847.038 2229.25,845.91 2230.25,844.806 2231.26,843.725 2232.26,842.667 \n",
       "  2233.27,841.632 2234.27,840.619 2235.28,839.629 2236.28,838.661 2237.28,837.715 2238.29,836.79 2239.29,835.886 2240.3,835.003 2241.3,834.141 2242.31,833.3 \n",
       "  2243.31,832.478 2244.32,831.677 2245.32,830.896 2246.32,830.134 2247.33,829.392 2248.33,828.668 2249.34,827.964 2250.34,827.279 2251.35,826.612 2252.35,825.964 \n",
       "  2253.35,825.333 2254.36,824.721 2255.36,824.127 2256.37,823.55 2257.37,822.991 2258.38,822.45 2259.38,821.925 2260.39,821.418 2261.39,820.927 2262.39,820.453 \n",
       "  2263.4,819.996 2264.4,819.556 2265.41,819.131 2266.41,818.723 2267.42,818.331 2268.42,817.955 2269.42,817.595 2270.43,817.251 2271.43,816.923 2272.44,816.61 \n",
       "  2273.44,816.312 2274.45,816.03 2275.45,815.764 2276.45,815.512 2277.46,815.276 2278.46,815.055 2279.47,814.849 2280.47,814.658 2281.48,814.481 2282.48,814.32 \n",
       "  2283.49,814.173 2284.49,814.042 2285.49,813.925 2286.5,813.822 2287.5,813.735 2288.51,813.662 2289.51,813.603 2290.52,813.56 2291.52,813.53 2292.52,813.516 \n",
       "  \n",
       "  \"/>\n",
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       "  294.859,758.261 295.863,757.433 296.868,756.601 297.872,755.767 298.876,754.929 299.881,754.087 300.885,753.242 301.889,752.392 302.894,751.537 303.898,750.678 \n",
       "  304.902,749.814 305.907,748.945 306.911,748.07 307.915,747.189 308.92,746.302 309.924,745.409 310.929,744.509 311.933,743.602 312.937,742.688 313.942,741.766 \n",
       "  314.946,740.837 315.95,739.899 316.955,738.954 317.959,737.999 318.963,737.036 319.968,736.064 320.972,735.082 321.976,734.09 322.981,733.088 323.985,732.076 \n",
       "  324.99,731.053 325.994,730.019 326.998,728.973 328.003,727.916 329.007,726.848 330.011,725.766 331.016,724.673 332.02,723.566 333.024,722.446 334.029,721.313 \n",
       "  335.033,720.166 336.037,719.004 337.042,717.828 338.046,716.637 339.051,715.431 340.055,714.209 341.059,712.972 342.064,711.718 343.068,710.447 344.072,709.16 \n",
       "  345.077,707.855 346.081,706.532 347.085,705.192 348.09,703.832 349.094,702.455 350.098,701.057 351.103,699.641 352.107,698.204 353.112,696.747 354.116,695.27 \n",
       "  355.12,693.771 356.125,692.251 357.129,690.709 358.133,689.144 359.138,687.557 360.142,685.947 361.146,684.313 362.151,682.656 363.155,680.974 364.159,679.267 \n",
       "  365.164,677.536 366.168,675.779 367.173,673.995 368.177,672.186 369.181,670.35 370.186,668.486 371.19,666.595 372.194,664.676 373.199,662.728 374.203,660.752 \n",
       "  375.207,658.746 376.212,656.711 377.216,654.645 378.22,652.549 379.225,650.421 380.229,648.263 381.234,646.072 382.238,643.85 383.242,641.594 384.247,639.306 \n",
       "  385.251,636.984 386.255,634.628 387.26,632.238 388.264,629.814 389.268,627.354 390.273,624.858 391.277,622.327 392.281,619.76 393.286,617.156 394.29,614.515 \n",
       "  395.295,611.837 396.299,609.121 397.303,606.367 398.308,603.574 399.312,600.743 400.316,597.873 401.321,594.964 402.325,592.015 403.329,589.026 404.334,585.997 \n",
       "  405.338,582.927 406.342,579.817 407.347,576.666 408.351,573.473 409.356,570.24 410.36,566.965 411.364,563.648 412.369,560.289 413.373,556.888 414.377,553.445 \n",
       "  415.382,549.96 416.386,546.433 417.39,542.863 418.395,539.251 419.399,535.596 420.403,531.9 421.408,528.16 422.412,524.379 423.417,520.555 424.421,516.69 \n",
       "  425.425,512.782 426.43,508.833 427.434,504.842 428.438,500.81 429.443,496.737 430.447,492.623 431.451,488.468 432.456,484.274 433.46,480.04 434.464,475.767 \n",
       "  435.469,471.455 436.473,467.105 437.478,462.717 438.482,458.293 439.486,453.831 440.491,449.334 441.495,444.802 442.499,440.236 443.504,435.636 444.508,431.003 \n",
       "  445.512,426.339 446.517,421.643 447.521,416.918 448.525,412.164 449.53,407.382 450.534,402.573 451.539,397.738 452.543,392.879 453.547,387.997 454.552,383.093 \n",
       "  455.556,378.168 456.56,373.224 457.565,368.262 458.569,363.284 459.573,358.291 460.578,353.285 461.582,348.267 462.586,343.239 463.591,338.203 464.595,333.16 \n",
       "  465.599,328.113 466.604,323.062 467.608,318.011 468.613,312.96 469.617,307.912 470.621,302.869 471.626,297.832 472.63,292.805 473.634,287.788 474.639,282.785 \n",
       "  475.643,277.797 476.647,272.826 477.652,267.876 478.656,262.947 479.66,258.043 480.665,253.165 481.669,248.316 482.674,243.499 483.678,238.716 484.682,233.969 \n",
       "  485.687,229.26 486.691,224.592 487.695,219.969 488.7,215.391 489.704,210.861 490.708,206.383 491.713,201.958 492.717,197.589 493.721,193.278 494.726,189.028 \n",
       "  495.73,184.842 496.735,180.722 497.739,176.669 498.743,172.688 499.748,168.78 500.752,164.947 501.756,161.192 502.761,157.517 503.765,153.925 504.769,150.417 \n",
       "  505.774,146.997 506.778,143.666 507.782,140.426 508.787,137.28 509.791,134.229 510.796,131.276 511.8,128.423 512.804,125.671 513.809,123.022 514.813,120.479 \n",
       "  515.817,118.043 516.822,115.715 517.826,113.497 518.83,111.391 519.835,109.398 520.839,107.52 521.843,105.758 522.848,104.113 523.852,102.586 524.857,101.179 \n",
       "  525.861,99.8917 526.865,98.7261 527.87,97.6825 528.874,96.7619 529.878,95.9649 530.883,95.2919 531.887,94.7436 532.891,94.3203 533.896,94.0224 534.9,93.8499 \n",
       "  535.904,93.8032 536.909,93.8821 537.913,94.0867 538.918,94.4167 539.922,94.8721 540.926,95.4523 541.931,96.1571 542.935,96.9858 543.939,97.938 544.944,99.0128 \n",
       "  545.948,100.21 546.952,101.528 547.957,102.966 548.961,104.523 549.965,106.198 550.97,107.99 551.974,109.898 552.979,111.92 553.983,114.054 554.987,116.301 \n",
       "  555.992,118.656 556.996,121.12 558,123.691 559.005,126.366 560.009,129.144 561.013,132.023 562.018,135.002 563.022,138.077 564.026,141.248 565.031,144.511 \n",
       "  566.035,147.865 567.04,151.309 568.044,154.838 569.048,158.452 570.053,162.148 571.057,165.923 572.061,169.776 573.066,173.703 574.07,177.703 575.074,181.773 \n",
       "  576.079,185.911 577.083,190.114 578.087,194.38 579.092,198.706 580.096,203.09 581.101,207.529 582.105,212.021 583.109,216.564 584.114,221.154 585.118,225.79 \n",
       "  586.122,230.468 587.127,235.187 588.131,239.945 589.135,244.737 590.14,249.563 591.144,254.42 592.148,259.305 593.153,264.216 594.157,269.151 595.162,274.108 \n",
       "  596.166,279.084 597.17,284.076 598.175,289.084 599.179,294.104 600.183,299.134 601.188,304.173 602.192,309.218 603.196,314.268 604.201,319.32 605.205,324.372 \n",
       "  606.209,329.422 607.214,334.469 608.218,339.511 609.223,344.546 610.227,349.572 611.231,354.588 612.236,359.592 613.24,364.582 614.244,369.556 615.249,374.514 \n",
       "  616.253,379.454 617.257,384.375 618.262,389.274 619.266,394.151 620.27,399.005 621.275,403.834 622.279,408.637 623.284,413.413 624.288,418.16 625.292,422.879 \n",
       "  626.297,427.567 627.301,432.225 628.305,436.85 629.31,441.442 630.314,446.001 631.318,450.525 632.323,455.014 633.327,459.467 634.331,463.883 635.336,468.262 \n",
       "  636.34,472.603 637.345,476.906 638.349,481.17 639.353,485.395 640.358,489.58 641.362,493.725 642.366,497.83 643.371,501.893 644.375,505.916 645.379,509.897 \n",
       "  646.384,513.837 647.388,517.735 648.392,521.591 649.397,525.405 650.401,529.177 651.406,532.906 652.41,536.593 653.414,540.238 654.419,543.841 655.423,547.401 \n",
       "  656.427,550.918 657.432,554.394 658.436,557.827 659.44,561.219 660.445,564.568 661.449,567.875 662.453,571.141 663.458,574.366 664.462,577.549 665.467,580.691 \n",
       "  666.471,583.792 667.475,586.853 668.48,589.873 669.484,592.853 670.488,595.793 671.493,598.694 672.497,601.556 673.501,604.379 674.506,607.163 675.51,609.908 \n",
       "  676.514,612.616 677.519,615.287 678.523,617.92 679.528,620.516 680.532,623.076 681.536,625.599 682.541,628.087 683.545,630.54 684.549,632.957 685.554,635.341 \n",
       "  686.558,637.689 687.562,640.005 688.567,642.286 689.571,644.535 690.575,646.752 691.58,648.936 692.584,651.089 693.589,653.21 694.593,655.3 695.597,657.361 \n",
       "  696.602,659.391 697.606,661.391 698.61,663.362 699.615,665.305 700.619,667.219 701.623,669.106 702.628,670.964 703.632,672.796 704.636,674.601 705.641,676.38 \n",
       "  706.645,678.134 707.65,679.861 708.654,681.564 709.658,683.243 710.663,684.897 711.667,686.527 712.671,688.134 713.676,689.718 714.68,691.28 715.684,692.819 \n",
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       "  726.732,708.405 727.737,709.709 728.741,710.996 729.745,712.266 730.75,713.52 731.754,714.757 732.758,715.979 733.763,717.185 734.767,718.377 735.771,719.553 \n",
       "  736.776,720.715 737.78,721.863 738.785,722.998 739.789,724.119 740.793,725.227 741.798,726.322 742.802,727.405 743.806,728.475 744.811,729.534 745.815,730.582 \n",
       "  746.819,731.618 747.824,732.644 748.828,733.659 749.832,734.663 750.837,735.658 751.841,736.644 752.846,737.619 753.85,738.586 754.854,739.544 755.859,740.494 \n",
       "  756.863,741.436 757.867,742.369 758.872,743.295 759.876,744.214 760.88,745.126 761.885,746.031 762.889,746.929 763.893,747.822 764.898,748.708 765.902,749.589 \n",
       "  766.907,750.464 767.911,751.335 768.915,752.2 769.92,753.061 770.924,753.918 771.928,754.771 772.933,755.62 773.937,756.465 774.941,757.307 775.946,758.147 \n",
       "  776.95,758.983 777.954,759.817 778.959,760.649 779.963,761.479 780.968,762.307 781.972,763.134 782.976,763.96 783.981,764.784 784.985,765.609 785.989,766.432 \n",
       "  786.994,767.256 787.998,768.08 789.002,768.904 790.007,769.729 791.011,770.554 792.015,771.381 793.02,772.209 794.024,773.039 795.029,773.871 796.033,774.705 \n",
       "  797.037,775.542 798.042,776.381 799.046,777.223 800.05,778.069 801.055,778.918 802.059,779.77 803.063,780.627 804.068,781.488 805.072,782.353 806.076,783.224 \n",
       "  807.081,784.099 808.085,784.98 809.09,785.866 810.094,786.759 811.098,787.657 812.103,788.562 813.107,789.474 814.111,790.393 815.116,791.319 816.12,792.252 \n",
       "  817.124,793.194 818.129,794.144 819.133,795.102 820.137,796.069 821.142,797.044 822.146,798.03 823.151,799.024 824.155,800.029 825.159,801.044 826.164,802.07 \n",
       "  827.168,803.106 828.172,804.154 829.177,805.212 830.181,806.283 831.185,807.366 832.19,808.461 833.194,809.569 834.198,810.69 835.203,811.825 836.207,812.973 \n",
       "  837.212,814.135 838.216,815.312 839.22,816.503 840.225,817.709 841.229,818.931 842.233,820.169 843.238,821.423 844.242,822.693 845.246,823.98 846.251,825.284 \n",
       "  847.255,826.606 848.259,827.946 849.264,829.304 850.268,830.681 851.273,832.076 852.277,833.492 853.281,834.927 854.286,836.382 855.29,837.858 856.294,839.354 \n",
       "  857.299,840.872 858.303,842.412 859.307,843.974 860.312,845.559 861.316,847.166 862.32,848.797 863.325,850.452 864.329,852.131 865.334,853.834 866.338,855.563 \n",
       "  867.342,857.317 868.347,859.096 869.351,860.902 870.355,862.735 871.36,864.595 872.364,866.482 873.368,868.398 874.373,870.341 875.377,872.314 876.381,874.315 \n",
       "  877.386,876.347 878.39,878.408 879.395,880.5 880.399,882.623 881.403,884.777 882.408,886.963 883.412,889.181 884.416,891.432 885.421,893.715 886.425,896.033 \n",
       "  887.429,898.384 888.434,900.769 889.438,903.189 890.442,905.644 891.447,908.135 892.451,910.661 893.456,913.224 894.46,915.823 895.464,918.46 896.469,921.133 \n",
       "  897.473,923.845 898.477,926.594 899.482,929.382 900.486,932.209 901.49,935.075 902.495,937.98 903.499,940.925 904.503,943.91 905.508,946.936 906.512,950.001 \n",
       "  907.517,953.108 908.521,956.256 909.525,959.445 910.53,962.676 911.534,965.949 912.538,969.263 913.543,972.62 914.547,976.019 915.551,979.46 916.556,982.943 \n",
       "  917.56,986.47 918.564,990.039 919.569,993.65 920.573,997.305 921.578,1001 922.582,1004.74 923.586,1008.52 924.591,1012.35 925.595,1016.22 926.599,1020.13 \n",
       "  927.604,1024.08 928.608,1028.07 929.612,1032.11 930.617,1036.19 931.621,1040.31 932.625,1044.47 933.63,1048.67 934.634,1052.91 935.639,1057.19 936.643,1061.51 \n",
       "  937.647,1065.87 938.652,1070.27 939.656,1074.7 940.66,1079.17 941.665,1083.68 942.669,1088.23 943.673,1092.81 944.678,1097.42 945.682,1102.07 946.686,1106.75 \n",
       "  947.691,1111.47 948.695,1116.21 949.7,1120.98 950.704,1125.79 951.708,1130.62 952.713,1135.47 953.717,1140.36 954.721,1145.27 955.726,1150.2 956.73,1155.15 \n",
       "  957.734,1160.12 958.739,1165.11 959.743,1170.12 960.747,1175.15 961.752,1180.19 962.756,1185.24 963.76,1190.3 964.765,1195.38 965.769,1200.46 966.774,1205.55 \n",
       "  967.778,1210.64 968.782,1215.74 969.787,1220.83 970.791,1225.92 971.795,1231.02 972.8,1236.1 973.804,1241.18 974.808,1246.25 975.813,1251.31 976.817,1256.35 \n",
       "  977.821,1261.38 978.826,1266.39 979.83,1271.37 980.835,1276.34 981.839,1281.28 982.843,1286.19 983.848,1291.08 984.852,1295.93 985.856,1300.74 986.861,1305.52 \n",
       "  987.865,1310.26 988.869,1314.96 989.874,1319.61 990.878,1324.22 991.882,1328.77 992.887,1333.28 993.891,1337.73 994.896,1342.12 995.9,1346.45 996.904,1350.72 \n",
       "  997.909,1354.93 998.913,1359.07 999.917,1363.14 1000.92,1367.14 1001.93,1371.06 1002.93,1374.91 1003.93,1378.68 1004.94,1382.36 1005.94,1385.97 1006.95,1389.48 \n",
       "  1007.95,1392.91 1008.96,1396.25 1009.96,1399.49 1010.97,1402.64 1011.97,1405.69 1012.97,1408.65 1013.98,1411.5 1014.98,1414.25 1015.99,1416.9 1016.99,1419.44 \n",
       "  1018,1421.87 1019,1424.19 1020,1426.4 1021.01,1428.49 1022.01,1430.47 1023.02,1432.34 1024.02,1434.09 1025.03,1435.72 1026.03,1437.23 1027.03,1438.62 \n",
       "  1028.04,1439.89 1029.04,1441.03 1030.05,1442.05 1031.05,1442.95 1032.06,1443.72 1033.06,1444.37 1034.07,1444.89 1035.07,1445.29 1036.07,1445.56 1037.08,1445.7 \n",
       "  1038.08,1445.72 1039.09,1445.6 1040.09,1445.37 1041.1,1445 1042.1,1444.51 1043.1,1443.9 1044.11,1443.15 1045.11,1442.29 1046.12,1441.3 1047.12,1440.18 \n",
       "  1048.13,1438.94 1049.13,1437.58 1050.14,1436.1 1051.14,1434.5 1052.14,1432.78 1053.15,1430.95 1054.15,1428.99 1055.16,1426.93 1056.16,1424.75 1057.17,1422.45 \n",
       "  1058.17,1420.05 1059.17,1417.54 1060.18,1414.92 1061.18,1412.19 1062.19,1409.37 1063.19,1406.44 1064.2,1403.41 1065.2,1400.28 1066.2,1397.06 1067.21,1393.75 \n",
       "  1068.21,1390.34 1069.22,1386.85 1070.22,1383.26 1071.23,1379.6 1072.23,1375.85 1073.24,1372.02 1074.24,1368.12 1075.24,1364.14 1076.25,1360.09 1077.25,1355.96 \n",
       "  1078.26,1351.77 1079.26,1347.52 1080.27,1343.2 1081.27,1338.82 1082.27,1334.39 1083.28,1329.89 1084.28,1325.35 1085.29,1320.76 1086.29,1316.12 1087.3,1311.43 \n",
       "  1088.3,1306.7 1089.31,1301.93 1090.31,1297.12 1091.31,1292.28 1092.32,1287.4 1093.32,1282.5 1094.33,1277.56 1095.33,1272.6 1096.34,1267.62 1097.34,1262.62 \n",
       "  1098.34,1257.59 1099.35,1252.55 1100.35,1247.5 1101.36,1242.43 1102.36,1237.36 1103.37,1232.27 1104.37,1227.18 1105.37,1222.09 1106.38,1216.99 1107.38,1211.9 \n",
       "  1108.39,1206.8 1109.39,1201.72 1110.4,1196.63 1111.4,1191.56 1112.41,1186.49 1113.41,1181.43 1114.41,1176.39 1115.42,1171.36 1116.42,1166.35 1117.43,1161.35 \n",
       "  1118.43,1156.37 1119.44,1151.41 1120.44,1146.48 1121.44,1141.56 1122.45,1136.67 1123.45,1131.81 1124.46,1126.97 1125.46,1122.16 1126.47,1117.38 1127.47,1112.63 \n",
       "  1128.48,1107.91 1129.48,1103.22 1130.48,1098.56 1131.49,1093.94 1132.49,1089.35 1133.5,1084.8 1134.5,1080.28 1135.51,1075.79 1136.51,1071.35 1137.51,1066.94 \n",
       "  1138.52,1062.57 1139.52,1058.24 1140.53,1053.95 1141.53,1049.7 1142.54,1045.49 1143.54,1041.32 1144.54,1037.19 1145.55,1033.1 1146.55,1029.05 1147.56,1025.05 \n",
       "  1148.56,1021.09 1149.57,1017.17 1150.57,1013.29 1151.58,1009.45 1152.58,1005.66 1153.58,1001.91 1154.59,998.198 1155.59,994.533 1156.6,990.91 1157.6,987.33 \n",
       "  1158.61,983.793 1159.61,980.298 1160.61,976.846 1161.62,973.437 1162.62,970.069 1163.63,966.744 1164.63,963.46 1165.64,960.219 1166.64,957.019 1167.64,953.86 \n",
       "  1168.65,950.743 1169.65,947.666 1170.66,944.63 1171.66,941.635 1172.67,938.68 1173.67,935.764 1174.68,932.888 1175.68,930.051 1176.68,927.253 1177.69,924.493 \n",
       "  1178.69,921.772 1179.7,919.088 1180.7,916.442 1181.71,913.833 1182.71,911.261 1183.71,908.725 1184.72,906.225 1185.72,903.76 1186.73,901.331 1187.73,898.937 \n",
       "  1188.74,896.576 1189.74,894.25 1190.75,891.957 1191.75,889.698 1192.75,887.471 1193.76,885.277 1194.76,883.114 1195.77,880.983 1196.77,878.882 1197.78,876.813 \n",
       "  1198.78,874.773 1199.78,872.763 1200.79,870.783 1201.79,868.832 1202.8,866.909 1203.8,865.014 1204.81,863.146 1205.81,861.306 1206.81,859.493 1207.82,857.706 \n",
       "  1208.82,855.944 1209.83,854.209 1210.83,852.498 1211.84,850.812 1212.84,849.151 1213.85,847.513 1214.85,845.899 1215.85,844.308 1216.86,842.739 1217.86,841.193 \n",
       "  1218.87,839.668 1219.87,838.165 1220.88,836.683 1221.88,835.222 1222.88,833.781 1223.89,832.36 1224.89,830.958 1225.9,829.575 1226.9,828.211 1227.91,826.866 \n",
       "  1228.91,825.538 1229.92,824.229 1230.92,822.936 1231.92,821.66 1232.93,820.401 1233.93,819.158 1234.94,817.931 1235.94,816.72 1236.95,815.523 1237.95,814.342 \n",
       "  1238.95,813.174 1239.96,812.021 1240.96,810.882 1241.97,809.756 1242.97,808.643 1243.98,807.543 1244.98,806.456 1245.98,805.38 1246.99,804.317 1247.99,803.265 \n",
       "  1249,802.224 1250,801.194 1251.01,800.175 1252.01,799.166 1253.02,798.167 1254.02,797.177 1255.02,796.197 1256.03,795.226 1257.03,794.264 1258.04,793.31 \n",
       "  1259.04,792.364 1260.05,791.427 1261.05,790.497 1262.05,789.574 1263.06,788.658 1264.06,787.749 1265.07,786.847 1266.07,785.951 1267.08,785.06 1268.08,784.176 \n",
       "  1269.08,783.296 1270.09,782.422 1271.09,781.553 1272.1,780.688 1273.1,779.828 1274.11,778.972 1275.11,778.119 1276.12,777.27 1277.12,776.424 1278.12,775.581 \n",
       "  1279.13,774.741 1280.13,773.903 1281.14,773.068 1282.14,772.235 1283.15,771.403 1284.15,770.572 1285.15,769.743 1286.16,768.915 1287.16,768.087 1288.17,767.26 \n",
       "  1289.17,766.432 1290.18,765.605 1291.18,764.777 1292.19,763.949 1293.19,763.12 1294.19,762.289 1295.2,761.457 1296.2,760.624 1297.21,759.788 1298.21,758.951 \n",
       "  1299.22,758.111 1300.22,757.268 1301.22,756.422 1302.23,755.573 1303.23,754.72 1304.24,753.864 1305.24,753.004 1306.25,752.139 1307.25,751.27 1308.25,750.396 \n",
       "  1309.26,749.516 1310.26,748.632 1311.27,747.741 1312.27,746.845 1313.28,745.943 1314.28,745.034 1315.29,744.118 1316.29,743.195 1317.29,742.265 1318.3,741.328 \n",
       "  1319.3,740.382 1320.31,739.428 1321.31,738.466 1322.32,737.495 1323.32,736.515 1324.32,735.525 1325.33,734.526 1326.33,733.517 1327.34,732.498 1328.34,731.468 \n",
       "  1329.35,730.427 1330.35,729.375 1331.36,728.312 1332.36,727.236 1333.36,726.149 1334.37,725.049 1335.37,723.936 1336.38,722.81 1337.38,721.671 1338.39,720.518 \n",
       "  1339.39,719.35 1340.39,718.169 1341.4,716.972 1342.4,715.761 1343.41,714.534 1344.41,713.291 1345.42,712.032 1346.42,710.756 1347.42,709.463 1348.43,708.154 \n",
       "  1349.43,706.826 1350.44,705.481 1351.44,704.117 1352.45,702.734 1353.45,701.332 1354.46,699.911 1355.46,698.47 1356.46,697.009 1357.47,695.527 1358.47,694.024 \n",
       "  1359.48,692.499 1360.48,690.953 1361.49,689.384 1362.49,687.793 1363.49,686.179 1364.5,684.541 1365.5,682.88 1366.51,681.194 1367.51,679.483 1368.52,677.748 \n",
       "  1369.52,675.986 1370.53,674.199 1371.53,672.386 1372.53,670.546 1373.54,668.678 1374.54,666.783 1375.55,664.86 1376.55,662.909 1377.56,660.928 1378.56,658.919 \n",
       "  1379.56,656.879 1380.57,654.81 1381.57,652.709 1382.58,650.578 1383.58,648.415 1384.59,646.221 1385.59,643.994 1386.59,641.734 1387.6,639.442 1388.6,637.116 \n",
       "  1389.61,634.755 1390.61,632.361 1391.62,629.932 1392.62,627.467 1393.63,624.967 1394.63,622.431 1395.63,619.859 1396.64,617.25 1397.64,614.604 1398.65,611.92 \n",
       "  1399.65,609.199 1400.66,606.439 1401.66,603.641 1402.66,600.804 1403.67,597.928 1404.67,595.012 1405.68,592.057 1406.68,589.061 1407.69,586.026 1408.69,582.949 \n",
       "  1409.69,579.832 1410.7,576.673 1411.7,573.473 1412.71,570.232 1413.71,566.948 1414.72,563.623 1415.72,560.255 1416.73,556.846 1417.73,553.393 1418.73,549.899 \n",
       "  1419.74,546.362 1420.74,542.782 1421.75,539.159 1422.75,535.493 1423.76,531.785 1424.76,528.034 1425.76,524.241 1426.77,520.405 1427.77,516.526 1428.78,512.605 \n",
       "  1429.78,508.642 1430.79,504.637 1431.79,500.59 1432.8,496.502 1433.8,492.372 1434.8,488.202 1435.81,483.991 1436.81,479.74 1437.82,475.449 1438.82,471.118 \n",
       "  1439.83,466.749 1440.83,462.342 1441.83,457.897 1442.84,453.415 1443.84,448.897 1444.85,444.342 1445.85,439.753 1446.86,435.13 1447.86,430.473 1448.86,425.783 \n",
       "  1449.87,421.062 1450.87,416.311 1451.88,411.529 1452.88,406.719 1453.89,401.881 1454.89,397.017 1455.9,392.128 1456.9,387.215 1457.9,382.278 1458.91,377.321 \n",
       "  1459.91,372.343 1460.92,367.346 1461.92,362.333 1462.93,357.303 1463.93,352.26 1464.93,347.204 1465.94,342.137 1466.94,337.06 1467.95,331.977 1468.95,326.887 \n",
       "  1469.96,321.794 1470.96,316.698 1471.97,311.603 1472.97,306.509 1473.97,301.419 1474.98,296.335 1475.98,291.259 1476.99,286.192 1477.99,281.138 1479,276.099 \n",
       "  1480,271.075 1481,266.071 1482.01,261.088 1483.01,256.128 1484.02,251.194 1485.02,246.288 1486.03,241.412 1487.03,236.57 1488.03,231.762 1489.04,226.993 \n",
       "  1490.04,222.263 1491.05,217.577 1492.05,212.935 1493.06,208.341 1494.06,203.797 1495.07,199.306 1496.07,194.871 1497.07,190.492 1498.08,186.174 1499.08,181.919 \n",
       "  1500.09,177.729 1501.09,173.606 1502.1,169.554 1503.1,165.574 1504.1,161.669 1505.11,157.841 1506.11,154.094 1507.12,150.428 1508.12,146.847 1509.13,143.352 \n",
       "  1510.13,139.946 1511.13,136.631 1512.14,133.41 1513.14,130.284 1514.15,127.255 1515.15,124.326 1516.16,121.499 1517.16,118.774 1518.17,116.155 1519.17,113.643 \n",
       "  1520.17,111.24 1521.18,108.947 1522.18,106.765 1523.19,104.698 1524.19,102.745 1525.2,100.908 1526.2,99.1889 1527.2,97.5886 1528.21,96.1082 1529.21,94.7487 \n",
       "  1530.22,93.5111 1531.22,92.3964 1532.23,91.4052 1533.23,90.5383 1534.24,89.7964 1535.24,89.1799 1536.24,88.6894 1537.25,88.3251 1538.25,88.0873 1539.26,87.9763 \n",
       "  1540.26,87.992 1541.27,88.1345 1542.27,88.4037 1543.27,88.7993 1544.28,89.3211 1545.28,89.9687 1546.29,90.7417 1547.29,91.6395 1548.3,92.6613 1549.3,93.8066 \n",
       "  1550.3,95.0745 1551.31,96.4641 1552.31,97.9744 1553.32,99.6043 1554.32,101.353 1555.33,103.218 1556.33,105.2 1557.34,107.296 1558.34,109.505 1559.34,111.825 \n",
       "  1560.35,114.256 1561.35,116.795 1562.36,119.44 1563.36,122.19 1564.37,125.043 1565.37,127.997 1566.37,131.05 1567.38,134.2 1568.38,137.444 1569.39,140.782 \n",
       "  1570.39,144.21 1571.4,147.726 1572.4,151.329 1573.41,155.015 1574.41,158.783 1575.41,162.63 1576.42,166.553 1577.42,170.551 1578.43,174.621 1579.43,178.761 \n",
       "  1580.44,182.967 1581.44,187.238 1582.44,191.571 1583.45,195.964 1584.45,200.414 1585.46,204.918 1586.46,209.474 1587.47,214.08 1588.47,218.733 1589.47,223.43 \n",
       "  1590.48,228.17 1591.48,232.949 1592.49,237.765 1593.49,242.616 1594.5,247.499 1595.5,252.412 1596.51,257.353 1597.51,262.318 1598.51,267.307 1599.52,272.316 \n",
       "  1600.52,277.343 1601.53,282.386 1602.53,287.444 1603.54,292.512 1604.54,297.59 1605.54,302.676 1606.55,307.767 1607.55,312.861 1608.56,317.957 1609.56,323.052 \n",
       "  1610.57,328.144 1611.57,333.232 1612.58,338.314 1613.58,343.388 1614.58,348.452 1615.59,353.505 1616.59,358.545 1617.6,363.571 1618.6,368.58 1619.61,373.571 \n",
       "  1620.61,378.544 1621.61,383.496 1622.62,388.427 1623.62,393.334 1624.63,398.217 1625.63,403.074 1626.64,407.905 1627.64,412.708 1628.64,417.482 1629.65,422.226 \n",
       "  1630.65,426.939 1631.66,431.62 1632.66,436.268 1633.67,440.883 1634.67,445.463 1635.68,450.008 1636.68,454.518 1637.68,458.99 1638.69,463.426 1639.69,467.823 \n",
       "  1640.7,472.182 1641.7,476.503 1642.71,480.783 1643.71,485.024 1644.71,489.225 1645.72,493.385 1646.72,497.504 1647.73,501.582 1648.73,505.618 1649.74,509.612 \n",
       "  1650.74,513.565 1651.74,517.475 1652.75,521.342 1653.75,525.168 1654.76,528.95 1655.76,532.69 1656.77,536.387 1657.77,540.042 1658.78,543.653 1659.78,547.222 \n",
       "  1660.78,550.749 1661.79,554.232 1662.79,557.673 1663.8,561.072 1664.8,564.429 1665.81,567.743 1666.81,571.016 1667.81,574.247 1668.82,577.436 1669.82,580.584 \n",
       "  1670.83,583.69 1671.83,586.756 1672.84,589.782 1673.84,592.767 1674.85,595.712 1675.85,598.617 1676.85,601.483 1677.86,604.31 1678.86,607.098 1679.87,609.847 \n",
       "  1680.87,612.559 1681.88,615.232 1682.88,617.869 1683.88,620.468 1684.89,623.031 1685.89,625.557 1686.9,628.048 1687.9,630.503 1688.91,632.923 1689.91,635.308 \n",
       "  1690.91,637.659 1691.92,639.977 1692.92,642.26 1693.93,644.511 1694.93,646.729 1695.94,648.915 1696.94,651.069 1697.95,653.192 1698.95,655.284 1699.95,657.345 \n",
       "  1700.96,659.377 1701.96,661.378 1702.97,663.351 1703.97,665.294 1704.98,667.21 1705.98,669.097 1706.98,670.957 1707.99,672.789 1708.99,674.595 1710,676.375 \n",
       "  1711,678.129 1712.01,679.858 1713.01,681.561 1714.02,683.24 1715.02,684.895 1716.02,686.525 1717.03,688.133 1718.03,689.718 1719.04,691.28 1720.04,692.82 \n",
       "  1721.05,694.338 1722.05,695.834 1723.05,697.31 1724.06,698.765 1725.06,700.2 1726.07,701.616 1727.07,703.011 1728.08,704.388 1729.08,705.746 1730.08,707.086 \n",
       "  1731.09,708.408 1732.09,709.712 1733.1,710.999 1734.1,712.269 1735.11,713.523 1736.11,714.761 1737.12,715.982 1738.12,717.189 1739.12,718.38 1740.13,719.557 \n",
       "  1741.13,720.719 1742.14,721.867 1743.14,723.002 1744.15,724.123 1745.15,725.231 1746.15,726.326 1747.16,727.409 1748.16,728.479 1749.17,729.538 1750.17,730.586 \n",
       "  1751.18,731.622 1752.18,732.648 1753.18,733.663 1754.19,734.667 1755.19,735.662 1756.2,736.648 1757.2,737.623 1758.21,738.59 1759.21,739.548 1760.22,740.498 \n",
       "  1761.22,741.439 1762.22,742.373 1763.23,743.299 1764.23,744.218 1765.24,745.13 1766.24,746.035 1767.25,746.933 1768.25,747.826 1769.25,748.712 1770.26,749.593 \n",
       "  1771.26,750.468 1772.27,751.339 1773.27,752.204 1774.28,753.065 1775.28,753.922 1776.29,754.774 1777.29,755.623 1778.29,756.469 1779.3,757.311 1780.3,758.15 \n",
       "  1781.31,758.987 1782.31,759.821 1783.32,760.653 1784.32,761.482 1785.32,762.311 1786.33,763.138 1787.33,763.963 1788.34,764.788 1789.34,765.612 1790.35,766.436 \n",
       "  1791.35,767.26 1792.35,768.083 1793.36,768.907 1794.36,769.732 1795.37,770.558 1796.37,771.385 1797.38,772.213 1798.38,773.043 1799.39,773.875 1800.39,774.709 \n",
       "  1801.39,775.545 1802.4,776.385 1803.4,777.227 1804.41,778.072 1805.41,778.921 1806.42,779.774 1807.42,780.631 1808.42,781.492 1809.43,782.357 1810.43,783.227 \n",
       "  1811.44,784.103 1812.44,784.984 1813.45,785.87 1814.45,786.763 1815.46,787.661 1816.46,788.566 1817.46,789.478 1818.47,790.397 1819.47,791.323 1820.48,792.256 \n",
       "  1821.48,793.198 1822.49,794.148 1823.49,795.106 1824.49,796.073 1825.5,797.048 1826.5,798.034 1827.51,799.028 1828.51,800.033 1829.52,801.048 1830.52,802.074 \n",
       "  1831.52,803.11 1832.53,804.158 1833.53,805.216 1834.54,806.287 1835.54,807.37 1836.55,808.465 1837.55,809.573 1838.56,810.694 1839.56,811.829 1840.56,812.977 \n",
       "  1841.57,814.139 1842.57,815.315 1843.58,816.507 1844.58,817.713 1845.59,818.935 1846.59,820.172 1847.59,821.426 1848.6,822.696 1849.6,823.983 1850.61,825.287 \n",
       "  1851.61,826.609 1852.62,827.948 1853.62,829.306 1854.63,830.683 1855.63,832.078 1856.63,833.493 1857.64,834.928 1858.64,836.383 1859.65,837.858 1860.65,839.355 \n",
       "  1861.66,840.873 1862.66,842.412 1863.66,843.974 1864.67,845.558 1865.67,847.165 1866.68,848.795 1867.68,850.449 1868.69,852.128 1869.69,853.831 1870.69,855.558 \n",
       "  1871.7,857.312 1872.7,859.091 1873.71,860.896 1874.71,862.728 1875.72,864.586 1876.72,866.473 1877.73,868.387 1878.73,870.33 1879.73,872.301 1880.74,874.301 \n",
       "  1881.74,876.331 1882.75,878.392 1883.75,880.482 1884.76,882.603 1885.76,884.756 1886.76,886.94 1887.77,889.157 1888.77,891.405 1889.78,893.687 1890.78,896.002 \n",
       "  1891.79,898.351 1892.79,900.734 1893.79,903.152 1894.8,905.605 1895.8,908.093 1896.81,910.616 1897.81,913.176 1898.82,915.772 1899.82,918.405 1900.83,921.076 \n",
       "  1901.83,923.784 1902.83,926.529 1903.84,929.313 1904.84,932.136 1905.85,934.998 1906.85,937.899 1907.86,940.839 1908.86,943.819 1909.86,946.839 1910.87,949.9 \n",
       "  1911.87,953.001 1912.88,956.143 1913.88,959.326 1914.89,962.551 1915.89,965.816 1916.9,969.124 1917.9,972.473 1918.9,975.865 1919.91,979.298 1920.91,982.773 \n",
       "  1921.92,986.291 1922.92,989.851 1923.93,993.454 1924.93,997.099 1925.93,1000.79 1926.94,1004.52 1927.94,1008.29 1928.95,1012.1 1929.95,1015.96 1930.96,1019.85 \n",
       "  1931.96,1023.79 1932.96,1027.78 1933.97,1031.8 1934.97,1035.86 1935.98,1039.97 1936.98,1044.11 1937.99,1048.3 1938.99,1052.52 1940,1056.79 1941,1061.09 \n",
       "  1942,1065.43 1943.01,1069.81 1944.01,1074.23 1945.02,1078.68 1946.02,1083.17 1947.03,1087.69 1948.03,1092.25 1949.03,1096.84 1950.04,1101.47 1951.04,1106.12 \n",
       "  1952.05,1110.81 1953.05,1115.53 1954.06,1120.28 1955.06,1125.06 1956.07,1129.86 1957.07,1134.69 1958.07,1139.54 1959.08,1144.42 1960.08,1149.32 1961.09,1154.24 \n",
       "  1962.09,1159.18 1963.1,1164.14 1964.1,1169.11 1965.1,1174.1 1966.11,1179.1 1967.11,1184.12 1968.12,1189.15 1969.12,1194.18 1970.13,1199.22 1971.13,1204.27 \n",
       "  1972.13,1209.32 1973.14,1214.37 1974.14,1219.42 1975.15,1224.47 1976.15,1229.52 1977.16,1234.56 1978.16,1239.59 1979.17,1244.61 1980.17,1249.62 1981.17,1254.61 \n",
       "  1982.18,1259.58 1983.18,1264.54 1984.19,1269.48 1985.19,1274.39 1986.2,1279.27 1987.2,1284.13 1988.2,1288.95 1989.21,1293.75 1990.21,1298.5 1991.22,1303.22 \n",
       "  1992.22,1307.9 1993.23,1312.54 1994.23,1317.13 1995.23,1321.67 1996.24,1326.16 1997.24,1330.6 1998.25,1334.99 1999.25,1339.31 2000.26,1343.58 2001.26,1347.78 \n",
       "  2002.27,1351.92 2003.27,1355.99 2004.27,1359.99 2005.28,1363.92 2006.28,1367.77 2007.29,1371.54 2008.29,1375.24 2009.3,1378.85 2010.3,1382.38 2011.3,1385.83 \n",
       "  2012.31,1389.18 2013.31,1392.44 2014.32,1395.61 2015.32,1398.69 2016.33,1401.67 2017.33,1404.55 2018.34,1407.33 2019.34,1410 2020.34,1412.57 2021.35,1415.04 \n",
       "  2022.35,1417.39 2023.36,1419.64 2024.36,1421.77 2025.37,1423.79 2026.37,1425.7 2027.37,1427.49 2028.38,1429.17 2029.38,1430.73 2030.39,1432.16 2031.39,1433.48 \n",
       "  2032.4,1434.68 2033.4,1435.75 2034.4,1436.71 2035.41,1437.53 2036.41,1438.24 2037.42,1438.82 2038.42,1439.28 2039.43,1439.61 2040.43,1439.81 2041.44,1439.89 \n",
       "  2042.44,1439.84 2043.44,1439.67 2044.45,1439.37 2045.45,1438.95 2046.46,1438.4 2047.46,1437.73 2048.47,1436.93 2049.47,1436.01 2050.47,1434.97 2051.48,1433.8 \n",
       "  2052.48,1432.51 2053.49,1431.11 2054.49,1429.58 2055.5,1427.93 2056.5,1426.17 2057.51,1424.29 2058.51,1422.3 2059.51,1420.19 2060.52,1417.98 2061.52,1415.65 \n",
       "  2062.53,1413.21 2063.53,1410.67 2064.54,1408.02 2065.54,1405.27 2066.54,1402.42 2067.55,1399.46 2068.55,1396.41 2069.56,1393.27 2070.56,1390.03 2071.57,1386.7 \n",
       "  2072.57,1383.27 2073.57,1379.77 2074.58,1376.18 2075.58,1372.5 2076.59,1368.75 2077.59,1364.91 2078.6,1361 2079.6,1357.02 2080.61,1352.97 2081.61,1348.85 \n",
       "  2082.61,1344.66 2083.62,1340.41 2084.62,1336.1 2085.63,1331.73 2086.63,1327.31 2087.64,1322.83 2088.64,1318.3 2089.64,1313.72 2090.65,1309.1 2091.65,1304.43 \n",
       "  2092.66,1299.72 2093.66,1294.98 2094.67,1290.19 2095.67,1285.38 2096.68,1280.53 2097.68,1275.65 2098.68,1270.74 2099.69,1265.82 2100.69,1260.87 2101.7,1255.89 \n",
       "  2102.7,1250.91 2103.71,1245.9 2104.71,1240.89 2105.71,1235.86 2106.72,1230.82 2107.72,1225.78 2108.73,1220.73 2109.73,1215.68 2110.74,1210.63 2111.74,1205.58 \n",
       "  2112.74,1200.53 2113.75,1195.49 2114.75,1190.45 2115.76,1185.42 2116.76,1180.41 2117.77,1175.4 2118.77,1170.41 2119.78,1165.43 2120.78,1160.47 2121.78,1155.52 \n",
       "  2122.79,1150.6 2123.79,1145.69 2124.8,1140.81 2125.8,1135.95 2126.81,1131.12 2127.81,1126.31 2128.81,1121.53 2129.82,1116.77 2130.82,1112.05 2131.83,1107.35 \n",
       "  2132.83,1102.69 2133.84,1098.06 2134.84,1093.46 2135.84,1088.89 2136.85,1084.36 2137.85,1079.86 2138.86,1075.4 2139.86,1070.97 2140.87,1066.59 2141.87,1062.24 \n",
       "  2142.88,1057.92 2143.88,1053.65 2144.88,1049.42 2145.89,1045.22 2146.89,1041.07 2147.9,1036.96 2148.9,1032.88 2149.91,1028.85 2150.91,1024.86 2151.91,1020.91 \n",
       "  2152.92,1017 2153.92,1013.14 2154.93,1009.31 2155.93,1005.53 2156.94,1001.79 2157.94,998.096 2158.95,994.441 2159.95,990.829 2160.95,987.259 2161.96,983.732 \n",
       "  2162.96,980.247 2163.97,976.804 2164.97,973.403 2165.98,970.044 2166.98,966.727 2167.98,963.452 2168.99,960.219 2169.99,957.026 2171,953.875 2172,950.765 \n",
       "  2173.01,947.695 2174.01,944.666 2175.01,941.677 2176.02,938.728 2177.02,935.819 2178.03,932.949 2179.03,930.118 2180.04,927.325 2181.04,924.571 2182.05,921.855 \n",
       "  2183.05,919.177 2184.05,916.536 2185.06,913.932 2186.06,911.365 2187.07,908.834 2188.07,906.338 2189.08,903.878 2190.08,901.454 2191.08,899.064 2192.09,896.708 \n",
       "  2193.09,894.386 2194.1,892.098 2195.1,889.842 2196.11,887.62 2197.11,885.429 2198.12,883.27 2199.12,881.143 2200.12,879.047 2201.13,876.981 2202.13,874.946 \n",
       "  2203.14,872.94 2204.14,870.964 2205.15,869.016 2206.15,867.097 2207.15,865.206 2208.16,863.342 2209.16,861.506 2210.17,859.697 2211.17,857.913 2212.18,856.156 \n",
       "  2213.18,854.425 2214.18,852.718 2215.19,851.036 2216.19,849.379 2217.2,847.745 2218.2,846.135 2219.21,844.548 2220.21,842.983 2221.22,841.441 2222.22,839.921 \n",
       "  2223.22,838.422 2224.23,836.945 2225.23,835.488 2226.24,834.051 2227.24,832.635 2228.25,831.237 2229.25,829.86 2230.25,828.5 2231.26,827.16 2232.26,825.837 \n",
       "  2233.27,824.532 2234.27,823.245 2235.28,821.974 2236.28,820.72 2237.28,819.483 2238.29,818.261 2239.29,817.055 2240.3,815.864 2241.3,814.688 2242.31,813.526 \n",
       "  2243.31,812.379 2244.32,811.246 2245.32,810.126 2246.32,809.019 2247.33,807.926 2248.33,806.844 2249.34,805.776 2250.34,804.719 2251.35,803.673 2252.35,802.639 \n",
       "  2253.35,801.616 2254.36,800.604 2255.36,799.602 2256.37,798.61 2257.37,797.628 2258.38,796.656 2259.38,795.693 2260.39,794.738 2261.39,793.793 2262.39,792.855 \n",
       "  2263.4,791.926 2264.4,791.004 2265.41,790.09 2266.41,789.183 2267.42,788.283 2268.42,787.39 2269.42,786.503 2270.43,785.622 2271.43,784.747 2272.44,783.878 \n",
       "  2273.44,783.014 2274.45,782.155 2275.45,781.3 2276.45,780.45 2277.46,779.605 2278.46,778.763 2279.47,777.925 2280.47,777.091 2281.48,776.259 2282.48,775.431 \n",
       "  2283.49,774.605 2284.49,773.782 2285.49,772.961 2286.5,772.142 2287.5,771.324 2288.51,770.508 2289.51,769.693 2290.52,768.879 2291.52,768.066 2292.52,767.252 \n",
       "  \n",
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     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "N = 2000\n",
    "xmax = 10.0\n",
    "xmin = -10.0\n",
    "xvec = range(xmin,xmax,length=N)\n",
    "V3(x) =  Vp(x,V0,xmax,xmin,5)\n",
    "mat_H2 = make_H1dp(N,xmax,xmin,V3) \n",
    "energy4p,mat_v2 = eigen(mat_H2)\n",
    "println(\"周期ポテンシャルの時のエネルギー\")\n",
    "println(energy4p[1:10])\n",
    "println(\"ポテンシャル一つの時のエネルギー\")\n",
    "println(energy[1:10])\n",
    "using Plots\n",
    "plot(xvec,[mat_v2[:,1:4]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ポテンシャルが四つあるので、低エネルギーの解は四つある。それぞれが結合や反結合的な形で足し合わされているのが見てとれる。\n",
    "もともと四つのエネルギーが縮退していたが、縮退が解けた形になっている。\n",
    "このままどんどんポテンシャルの数を増やしていけば、固体っぽい何かになるかもしれない。\n",
    "しかし、ポテンシャルの数を増やせば増やすほど行列のサイズを大きくしていかなければならず、この方針はあまり筋が良くない。\n",
    "もともと原子核の周りに束縛されていた電子がどのように振る舞うかを見たいので、束縛された電子だけを考える、という方向でやってみよう。\n",
    "### 1.2 束縛状態だけを考えたシュレーディンガー方程式\n",
    "簡単のため、最初に考えていたようなポテンシャル二つのケースについて考えてみよう。シュレーディンガー方程式は\n",
    "$$\n",
    "\\left( -\\frac{d^2}{dx^2} + V_1(x) + V_2(x) \\right) \\psi(x) = \\epsilon \\psi(x)\n",
    "$$\n",
    "と書くことができる。\n",
    "ここで、\n",
    "$$\n",
    "V_1(x) = V_0 \\exp(-(x-x_0)^2)\n",
    "$$\n",
    "$$\n",
    "V_2(x) = V_0 \\exp(-(x+x_0)^2)\n",
    "$$\n",
    "である。\n",
    "もし、$x_0$が十分に大きいと、それぞれのポテンシャルの元に解いて得られた二つの束縛状態の解$\\psi_1(x)$,$\\psi_2(x)$はそれぞれ解である。\n",
    "次に、$x_0$を小さくしていく。解の形として、\n",
    "$$\n",
    "\\psi(x) = c_1 \\psi_1(x) + c_2 \\psi_2(x)\n",
    "$$\n",
    "を考えてみる。ここで、\n",
    "$$\n",
    "\\left( -\\frac{d^2}{dx^2} + V_1(x) \\right) \\psi_1(x) = \\epsilon_0 \\psi_1(x)\n",
    "$$\n",
    "$$\n",
    "\\left( -\\frac{d^2}{dx^2} + V_2(x) \\right) \\psi_2(x) = \\epsilon_0 \\psi_2(x)\n",
    "$$\n",
    "が成り立っている。\n",
    "仮定した解をシュレーディンガー方程式に代入すると、\n",
    "$$\n",
    "\\left( -\\frac{d^2}{dx^2} + V_1(x) + V_2(x) \\right) (c_1 \\psi_1(x) + c_2 \\psi_2(x)) = \\epsilon (c_1 \\psi_1(x) + c_2 \\psi_2(x))\n",
    "$$\n",
    "$$\n",
    "\\epsilon_0 c_1 \\psi_1(x)  + V_2(x) c_1 \\psi_1(x) + \\epsilon_0 c_2 \\psi_2(x)  + V_1(x) c_2 \\psi_2(x) = \\epsilon (c_1 \\psi_1(x) + c_2 \\psi_2(x))\n",
    "$$\n",
    "となり、$\\psi_1(x)^{\\ast}$を左からかけて全空間で積分すると、\n",
    "$$\n",
    "\\epsilon_0 c_1   +c_1 \\int |\\psi_1(x)|^2 V_2(x) dx    + c_2 \\int \\psi_1(x)^{\\ast} \\psi_2(x) V_1(x) dx +\\epsilon_0 c_2 \\int \\psi_1(x)^{\\ast} \\psi_2(x)dx = \\epsilon c_1 \n",
    "$$\n",
    "となり、$\\psi_2(x)^{\\ast}$を左からかけて全空間で積分すると、\n",
    "$$\n",
    "\\epsilon_0 c_1 \\int \\psi_2(x)^{\\ast} \\psi_1(x) dx+ c_1 \\int \\psi_2(x)^{\\ast} \\psi_1(x)V_2(x) dx + \\epsilon_0 c_2   + c_2 \\int V_1(x)|\\psi_2(x)|^2 dx= \\epsilon  c_2 \n",
    "$$\n",
    "となる。\n",
    "これらを行列表記すると、\n",
    "$$\n",
    "\\left( \n",
    "\\begin{matrix}\n",
    "\\epsilon_0 +\\int |\\psi_1(x)|^2 V_2(x)dx  & \\int \\psi_1(x)^{\\ast} \\psi_2(x) (V_1(x)+\\epsilon_0)dx \\\\\n",
    "\\int \\psi_2(x)^{\\ast} \\psi_1(x)( V_2(x)+\\epsilon_0) dx & \\epsilon_0 +\\int V_1(x)|\\psi_2(x)|^2 dx\n",
    "\\end{matrix}\n",
    "\\right)\n",
    "\\left( \n",
    "\\begin{matrix}\n",
    "c_1  \\\\\n",
    "c_2  \n",
    "\\end{matrix}\n",
    "\\right) = \\epsilon \\left( \n",
    "\\begin{matrix}\n",
    "c_1  \\\\\n",
    "c_2  \n",
    "\\end{matrix}\n",
    "\\right)\n",
    "$$\n",
    "となる。\n",
    "\n",
    "さて、この方程式も固有値問題となっている。Juliaで実際に計算してみよう。\n",
    "まず、$\\psi_1(x)$は"
   ]
  },
  {
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   "metadata": {},
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     "name": "stdout",
     "output_type": "stream",
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      "-3.1403506852520637\n"
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       "  566.035,87.9763 567.04,87.9763 568.044,87.9763 569.048,87.9763 570.053,87.9763 571.057,87.9763 572.061,87.9763 573.066,87.9763 574.07,87.9763 575.074,87.9763 \n",
       "  576.079,87.9763 577.083,87.9763 578.087,87.9763 579.092,87.9763 580.096,87.9763 581.101,87.9763 582.105,87.9763 583.109,87.9763 584.114,87.9763 585.118,87.9763 \n",
       "  586.122,87.9763 587.127,87.9763 588.131,87.9763 589.135,87.9763 590.14,87.9763 591.144,87.9763 592.148,87.9763 593.153,87.9763 594.157,87.9763 595.162,87.9763 \n",
       "  596.166,87.9763 597.17,87.9763 598.175,87.9763 599.179,87.9763 600.183,87.9763 601.188,87.9763 602.192,87.9763 603.196,87.9763 604.201,87.9763 605.205,87.9763 \n",
       "  606.209,87.9763 607.214,87.9763 608.218,87.9763 609.223,87.9763 610.227,87.9763 611.231,87.9763 612.236,87.9763 613.24,87.9763 614.244,87.9763 615.249,87.9763 \n",
       "  616.253,87.9763 617.257,87.9763 618.262,87.9763 619.266,87.9763 620.27,87.9763 621.275,87.9763 622.279,87.9763 623.284,87.9763 624.288,87.9763 625.292,87.9763 \n",
       "  626.297,87.9763 627.301,87.9763 628.305,87.9763 629.31,87.9763 630.314,87.9763 631.318,87.9763 632.323,87.9763 633.327,87.9763 634.331,87.9763 635.336,87.9763 \n",
       "  636.34,87.9763 637.345,87.9763 638.349,87.9764 639.353,87.9764 640.358,87.9764 641.362,87.9764 642.366,87.9764 643.371,87.9764 644.375,87.9764 645.379,87.9764 \n",
       "  646.384,87.9764 647.388,87.9764 648.392,87.9764 649.397,87.9764 650.401,87.9764 651.406,87.9764 652.41,87.9764 653.414,87.9764 654.419,87.9764 655.423,87.9764 \n",
       "  656.427,87.9764 657.432,87.9764 658.436,87.9764 659.44,87.9764 660.445,87.9764 661.449,87.9764 662.453,87.9764 663.458,87.9765 664.462,87.9765 665.467,87.9765 \n",
       "  666.471,87.9765 667.475,87.9765 668.48,87.9765 669.484,87.9765 670.488,87.9765 671.493,87.9765 672.497,87.9765 673.501,87.9765 674.506,87.9765 675.51,87.9765 \n",
       "  676.514,87.9765 677.519,87.9765 678.523,87.9765 679.528,87.9765 680.532,87.9766 681.536,87.9766 682.541,87.9766 683.545,87.9766 684.549,87.9766 685.554,87.9766 \n",
       "  686.558,87.9766 687.562,87.9766 688.567,87.9766 689.571,87.9766 690.575,87.9766 691.58,87.9766 692.584,87.9767 693.589,87.9767 694.593,87.9767 695.597,87.9767 \n",
       "  696.602,87.9767 697.606,87.9767 698.61,87.9767 699.615,87.9767 700.619,87.9767 701.623,87.9767 702.628,87.9768 703.632,87.9768 704.636,87.9768 705.641,87.9768 \n",
       "  706.645,87.9768 707.65,87.9768 708.654,87.9768 709.658,87.9768 710.663,87.9768 711.667,87.9769 712.671,87.9769 713.676,87.9769 714.68,87.9769 715.684,87.9769 \n",
       "  716.689,87.9769 717.693,87.9769 718.697,87.977 719.702,87.977 720.706,87.977 721.71,87.977 722.715,87.977 723.719,87.977 724.724,87.977 725.728,87.9771 \n",
       "  726.732,87.9771 727.737,87.9771 728.741,87.9771 729.745,87.9771 730.75,87.9771 731.754,87.9772 732.758,87.9772 733.763,87.9772 734.767,87.9772 735.771,87.9772 \n",
       "  736.776,87.9773 737.78,87.9773 738.785,87.9773 739.789,87.9773 740.793,87.9773 741.798,87.9774 742.802,87.9774 743.806,87.9774 744.811,87.9774 745.815,87.9775 \n",
       "  746.819,87.9775 747.824,87.9775 748.828,87.9775 749.832,87.9776 750.837,87.9776 751.841,87.9776 752.846,87.9776 753.85,87.9777 754.854,87.9777 755.859,87.9777 \n",
       "  756.863,87.9777 757.867,87.9778 758.872,87.9778 759.876,87.9778 760.88,87.9779 761.885,87.9779 762.889,87.9779 763.893,87.978 764.898,87.978 765.902,87.978 \n",
       "  766.907,87.9781 767.911,87.9781 768.915,87.9781 769.92,87.9782 770.924,87.9782 771.928,87.9782 772.933,87.9783 773.937,87.9783 774.941,87.9783 775.946,87.9784 \n",
       "  776.95,87.9784 777.954,87.9785 778.959,87.9785 779.963,87.9786 780.968,87.9786 781.972,87.9786 782.976,87.9787 783.981,87.9787 784.985,87.9788 785.989,87.9788 \n",
       "  786.994,87.9789 787.998,87.9789 789.002,87.979 790.007,87.979 791.011,87.9791 792.015,87.9791 793.02,87.9792 794.024,87.9792 795.029,87.9793 796.033,87.9794 \n",
       "  797.037,87.9794 798.042,87.9795 799.046,87.9795 800.05,87.9796 801.055,87.9797 802.059,87.9797 803.063,87.9798 804.068,87.9798 805.072,87.9799 806.076,87.98 \n",
       "  807.081,87.98 808.085,87.9801 809.09,87.9802 810.094,87.9803 811.098,87.9803 812.103,87.9804 813.107,87.9805 814.111,87.9806 815.116,87.9806 816.12,87.9807 \n",
       "  817.124,87.9808 818.129,87.9809 819.133,87.981 820.137,87.9811 821.142,87.9812 822.146,87.9812 823.151,87.9813 824.155,87.9814 825.159,87.9815 826.164,87.9816 \n",
       "  827.168,87.9817 828.172,87.9818 829.177,87.9819 830.181,87.982 831.185,87.9821 832.19,87.9822 833.194,87.9823 834.198,87.9825 835.203,87.9826 836.207,87.9827 \n",
       "  837.212,87.9828 838.216,87.9829 839.22,87.983 840.225,87.9832 841.229,87.9833 842.233,87.9834 843.238,87.9836 844.242,87.9837 845.246,87.9838 846.251,87.984 \n",
       "  847.255,87.9841 848.259,87.9842 849.264,87.9844 850.268,87.9845 851.273,87.9847 852.277,87.9848 853.281,87.985 854.286,87.9852 855.29,87.9853 856.294,87.9855 \n",
       "  857.299,87.9856 858.303,87.9858 859.307,87.986 860.312,87.9862 861.316,87.9863 862.32,87.9865 863.325,87.9867 864.329,87.9869 865.334,87.9871 866.338,87.9873 \n",
       "  867.342,87.9875 868.347,87.9877 869.351,87.9879 870.355,87.9881 871.36,87.9883 872.364,87.9885 873.368,87.9888 874.373,87.989 875.377,87.9892 876.381,87.9895 \n",
       "  877.386,87.9897 878.39,87.9899 879.395,87.9902 880.399,87.9904 881.403,87.9907 882.408,87.991 883.412,87.9912 884.416,87.9915 885.421,87.9918 886.425,87.992 \n",
       "  887.429,87.9923 888.434,87.9926 889.438,87.9929 890.442,87.9932 891.447,87.9935 892.451,87.9938 893.456,87.9941 894.46,87.9945 895.464,87.9948 896.469,87.9951 \n",
       "  897.473,87.9955 898.477,87.9958 899.482,87.9962 900.486,87.9965 901.49,87.9969 902.495,87.9973 903.499,87.9976 904.503,87.998 905.508,87.9984 906.512,87.9988 \n",
       "  907.517,87.9992 908.521,87.9996 909.525,88.0001 910.53,88.0005 911.534,88.0009 912.538,88.0014 913.543,88.0018 914.547,88.0023 915.551,88.0028 916.556,88.0032 \n",
       "  917.56,88.0037 918.564,88.0042 919.569,88.0047 920.573,88.0052 921.578,88.0057 922.582,88.0063 923.586,88.0068 924.591,88.0074 925.595,88.0079 926.599,88.0085 \n",
       "  927.604,88.0091 928.608,88.0097 929.612,88.0103 930.617,88.0109 931.621,88.0115 932.625,88.0121 933.63,88.0128 934.634,88.0134 935.639,88.0141 936.643,88.0148 \n",
       "  937.647,88.0155 938.652,88.0162 939.656,88.0169 940.66,88.0176 941.665,88.0183 942.669,88.0191 943.673,88.0199 944.678,88.0207 945.682,88.0214 946.686,88.0223 \n",
       "  947.691,88.0231 948.695,88.0239 949.7,88.0248 950.704,88.0257 951.708,88.0265 952.713,88.0274 953.717,88.0284 954.721,88.0293 955.726,88.0302 956.73,88.0312 \n",
       "  957.734,88.0322 958.739,88.0332 959.743,88.0342 960.747,88.0353 961.752,88.0363 962.756,88.0374 963.76,88.0385 964.765,88.0396 965.769,88.0407 966.774,88.0419 \n",
       "  967.778,88.0431 968.782,88.0443 969.787,88.0455 970.791,88.0467 971.795,88.048 972.8,88.0493 973.804,88.0506 974.808,88.0519 975.813,88.0533 976.817,88.0547 \n",
       "  977.821,88.0561 978.826,88.0575 979.83,88.0589 980.835,88.0604 981.839,88.0619 982.843,88.0635 983.848,88.065 984.852,88.0666 985.856,88.0682 986.861,88.0699 \n",
       "  987.865,88.0716 988.869,88.0733 989.874,88.075 990.878,88.0768 991.882,88.0786 992.887,88.0804 993.891,88.0823 994.896,88.0842 995.9,88.0861 996.904,88.0881 \n",
       "  997.909,88.0901 998.913,88.0921 999.917,88.0942 1000.92,88.0963 1001.93,88.0985 1002.93,88.1006 1003.93,88.1029 1004.94,88.1051 1005.94,88.1075 1006.95,88.1098 \n",
       "  1007.95,88.1122 1008.96,88.1146 1009.96,88.1171 1010.97,88.1196 1011.97,88.1222 1012.97,88.1248 1013.98,88.1275 1014.98,88.1302 1015.99,88.1329 1016.99,88.1357 \n",
       "  1018,88.1386 1019,88.1415 1020,88.1445 1021.01,88.1475 1022.01,88.1505 1023.02,88.1536 1024.02,88.1568 1025.03,88.1601 1026.03,88.1633 1027.03,88.1667 \n",
       "  1028.04,88.1701 1029.04,88.1736 1030.05,88.1771 1031.05,88.1807 1032.06,88.1844 1033.06,88.1881 1034.07,88.1919 1035.07,88.1957 1036.07,88.1997 1037.08,88.2037 \n",
       "  1038.08,88.2077 1039.09,88.2119 1040.09,88.2161 1041.1,88.2204 1042.1,88.2248 1043.1,88.2292 1044.11,88.2337 1045.11,88.2383 1046.12,88.243 1047.12,88.2478 \n",
       "  1048.13,88.2527 1049.13,88.2576 1050.14,88.2626 1051.14,88.2678 1052.14,88.273 1053.15,88.2783 1054.15,88.2837 1055.16,88.2892 1056.16,88.2948 1057.17,88.3005 \n",
       "  1058.17,88.3063 1059.17,88.3122 1060.18,88.3182 1061.18,88.3243 1062.19,88.3306 1063.19,88.3369 1064.2,88.3434 1065.2,88.3499 1066.2,88.3566 1067.21,88.3634 \n",
       "  1068.21,88.3704 1069.22,88.3774 1070.22,88.3846 1071.23,88.3919 1072.23,88.3993 1073.24,88.4069 1074.24,88.4146 1075.24,88.4225 1076.25,88.4304 1077.25,88.4386 \n",
       "  1078.26,88.4468 1079.26,88.4553 1080.27,88.4638 1081.27,88.4726 1082.27,88.4814 1083.28,88.4905 1084.28,88.4997 1085.29,88.509 1086.29,88.5186 1087.3,88.5283 \n",
       "  1088.3,88.5382 1089.31,88.5482 1090.31,88.5584 1091.31,88.5689 1092.32,88.5795 1093.32,88.5903 1094.33,88.6012 1095.33,88.6124 1096.34,88.6238 1097.34,88.6354 \n",
       "  1098.34,88.6472 1099.35,88.6592 1100.35,88.6714 1101.36,88.6838 1102.36,88.6965 1103.37,88.7094 1104.37,88.7225 1105.37,88.7358 1106.38,88.7494 1107.38,88.7633 \n",
       "  1108.39,88.7774 1109.39,88.7917 1110.4,88.8063 1111.4,88.8211 1112.41,88.8362 1113.41,88.8516 1114.41,88.8673 1115.42,88.8832 1116.42,88.8995 1117.43,88.916 \n",
       "  1118.43,88.9328 1119.44,88.9499 1120.44,88.9673 1121.44,88.985 1122.45,89.0031 1123.45,89.0215 1124.46,89.0402 1125.46,89.0592 1126.47,89.0786 1127.47,89.0983 \n",
       "  1128.48,89.1184 1129.48,89.1388 1130.48,89.1596 1131.49,89.1808 1132.49,89.2023 1133.5,89.2242 1134.5,89.2466 1135.51,89.2693 1136.51,89.2924 1137.51,89.316 \n",
       "  1138.52,89.3399 1139.52,89.3643 1140.53,89.3892 1141.53,89.4144 1142.54,89.4402 1143.54,89.4664 1144.54,89.493 1145.55,89.5201 1146.55,89.5478 1147.56,89.5759 \n",
       "  1148.56,89.6045 1149.57,89.6336 1150.57,89.6633 1151.58,89.6935 1152.58,89.7242 1153.58,89.7554 1154.59,89.7873 1155.59,89.8197 1156.6,89.8526 1157.6,89.8862 \n",
       "  1158.61,89.9204 1159.61,89.9552 1160.61,89.9906 1161.62,90.0266 1162.62,90.0633 1163.63,90.1006 1164.63,90.1386 1165.64,90.1773 1166.64,90.2167 1167.64,90.2567 \n",
       "  1168.65,90.2975 1169.65,90.3391 1170.66,90.3813 1171.66,90.4244 1172.67,90.4681 1173.67,90.5127 1174.68,90.5581 1175.68,90.6043 1176.68,90.6513 1177.69,90.6991 \n",
       "  1178.69,90.7479 1179.7,90.7974 1180.7,90.8479 1181.71,90.8993 1182.71,90.9516 1183.71,91.0048 1184.72,91.059 1185.72,91.1141 1186.73,91.1702 1187.73,91.2274 \n",
       "  1188.74,91.2855 1189.74,91.3447 1190.75,91.405 1191.75,91.4663 1192.75,91.5288 1193.76,91.5923 1194.76,91.657 1195.77,91.7228 1196.77,91.7898 1197.78,91.8581 \n",
       "  1198.78,91.9275 1199.78,91.9982 1200.79,92.0701 1201.79,92.1434 1202.8,92.2179 1203.8,92.2938 1204.81,92.371 1205.81,92.4496 1206.81,92.5297 1207.82,92.6111 \n",
       "  1208.82,92.694 1209.83,92.7784 1210.83,92.8643 1211.84,92.9518 1212.84,93.0408 1213.85,93.1313 1214.85,93.2236 1215.85,93.3174 1216.86,93.413 1217.86,93.5102 \n",
       "  1218.87,93.6092 1219.87,93.71 1220.88,93.8125 1221.88,93.9169 1222.88,94.0232 1223.89,94.1314 1224.89,94.2415 1225.9,94.3536 1226.9,94.4676 1227.91,94.5838 \n",
       "  1228.91,94.702 1229.92,94.8223 1230.92,94.9447 1231.92,95.0694 1232.93,95.1963 1233.93,95.3254 1234.94,95.4569 1235.94,95.5907 1236.95,95.7269 1237.95,95.8655 \n",
       "  1238.95,96.0067 1239.96,96.1503 1240.96,96.2965 1241.97,96.4454 1242.97,96.5969 1243.98,96.7511 1244.98,96.908 1245.98,97.0678 1246.99,97.2304 1247.99,97.396 \n",
       "  1249,97.5645 1250,97.736 1251.01,97.9106 1252.01,98.0883 1253.02,98.2692 1254.02,98.4533 1255.02,98.6407 1256.03,98.8315 1257.03,99.0256 1258.04,99.2233 \n",
       "  1259.04,99.4245 1260.05,99.6293 1261.05,99.8377 1262.05,100.05 1263.06,100.266 1264.06,100.486 1265.07,100.709 1266.07,100.937 1267.08,101.169 1268.08,101.405 \n",
       "  1269.08,101.645 1270.09,101.89 1271.09,102.139 1272.1,102.392 1273.1,102.65 1274.11,102.912 1275.11,103.179 1276.12,103.451 1277.12,103.728 1278.12,104.01 \n",
       "  1279.13,104.297 1280.13,104.589 1281.14,104.886 1282.14,105.188 1283.15,105.496 1284.15,105.81 1285.15,106.129 1286.16,106.453 1287.16,106.784 1288.17,107.12 \n",
       "  1289.17,107.463 1290.18,107.811 1291.18,108.166 1292.19,108.527 1293.19,108.895 1294.19,109.269 1295.2,109.65 1296.2,110.037 1297.21,110.432 1298.21,110.834 \n",
       "  1299.22,111.243 1300.22,111.659 1301.22,112.082 1302.23,112.514 1303.23,112.952 1304.24,113.399 1305.24,113.854 1306.25,114.317 1307.25,114.788 1308.25,115.267 \n",
       "  1309.26,115.756 1310.26,116.252 1311.27,116.758 1312.27,117.273 1313.28,117.797 1314.28,118.33 1315.29,118.873 1316.29,119.426 1317.29,119.988 1318.3,120.561 \n",
       "  1319.3,121.143 1320.31,121.736 1321.31,122.34 1322.32,122.955 1323.32,123.58 1324.32,124.217 1325.33,124.865 1326.33,125.525 1327.34,126.196 1328.34,126.88 \n",
       "  1329.35,127.575 1330.35,128.283 1331.36,129.004 1332.36,129.738 1333.36,130.484 1334.37,131.244 1335.37,132.018 1336.38,132.805 1337.38,133.607 1338.39,134.422 \n",
       "  1339.39,135.253 1340.39,136.098 1341.4,136.958 1342.4,137.834 1343.41,138.725 1344.41,139.632 1345.42,140.555 1346.42,141.495 1347.42,142.451 1348.43,143.425 \n",
       "  1349.43,144.415 1350.44,145.424 1351.44,146.45 1352.45,147.495 1353.45,148.558 1354.46,149.64 1355.46,150.742 1356.46,151.863 1357.47,153.004 1358.47,154.165 \n",
       "  1359.48,155.347 1360.48,156.55 1361.49,157.775 1362.49,159.021 1363.49,160.289 1364.5,161.579 1365.5,162.893 1366.51,164.23 1367.51,165.591 1368.52,166.975 \n",
       "  1369.52,168.384 1370.53,169.819 1371.53,171.278 1372.53,172.764 1373.54,174.275 1374.54,175.814 1375.55,177.379 1376.55,178.972 1377.56,180.593 1378.56,182.243 \n",
       "  1379.56,183.922 1380.57,185.631 1381.57,187.369 1382.58,189.138 1383.58,190.939 1384.59,192.77 1385.59,194.634 1386.59,196.531 1387.6,198.461 1388.6,200.424 \n",
       "  1389.61,202.422 1390.61,204.455 1391.62,206.524 1392.62,208.628 1393.63,210.769 1394.63,212.947 1395.63,215.163 1396.64,217.418 1397.64,219.712 1398.65,222.045 \n",
       "  1399.65,224.419 1400.66,226.834 1401.66,229.29 1402.66,231.789 1403.67,234.331 1404.67,236.916 1405.68,239.546 1406.68,242.221 1407.69,244.941 1408.69,247.708 \n",
       "  1409.69,250.522 1410.7,253.384 1411.7,256.295 1412.71,259.254 1413.71,262.264 1414.72,265.325 1415.72,268.437 1416.73,271.601 1417.73,274.819 1418.73,278.09 \n",
       "  1419.74,281.415 1420.74,284.797 1421.75,288.234 1422.75,291.728 1423.76,295.279 1424.76,298.889 1425.76,302.559 1426.77,306.288 1427.77,310.078 1428.78,313.93 \n",
       "  1429.78,317.844 1430.79,321.822 1431.79,325.863 1432.8,329.969 1433.8,334.141 1434.8,338.379 1435.81,342.684 1436.81,347.058 1437.82,351.5 1438.82,356.011 \n",
       "  1439.83,360.593 1440.83,365.246 1441.83,369.971 1442.84,374.768 1443.84,379.639 1444.85,384.584 1445.85,389.603 1446.86,394.698 1447.86,399.869 1448.86,405.118 \n",
       "  1449.87,410.443 1450.87,415.847 1451.88,421.33 1452.88,426.893 1453.89,432.535 1454.89,438.259 1455.9,444.064 1456.9,449.95 1457.9,455.919 1458.91,461.971 \n",
       "  1459.91,468.106 1460.92,474.326 1461.92,480.629 1462.93,487.017 1463.93,493.49 1464.93,500.049 1465.94,506.693 1466.94,513.423 1467.95,520.24 1468.95,527.142 \n",
       "  1469.96,534.131 1470.96,541.207 1471.97,548.369 1472.97,555.618 1473.97,562.954 1474.98,570.376 1475.98,577.885 1476.99,585.48 1477.99,593.161 1479,600.927 \n",
       "  1480,608.779 1481,616.716 1482.01,624.738 1483.01,632.843 1484.02,641.032 1485.02,649.303 1486.03,657.657 1487.03,666.091 1488.03,674.606 1489.04,683.201 \n",
       "  1490.04,691.874 1491.05,700.624 1492.05,709.45 1493.06,718.351 1494.06,727.326 1495.07,736.373 1496.07,745.49 1497.07,754.677 1498.08,763.931 1499.08,773.251 \n",
       "  1500.09,782.635 1501.09,792.081 1502.1,801.587 1503.1,811.151 1504.1,820.771 1505.11,830.444 1506.11,840.168 1507.12,849.941 1508.12,859.759 1509.13,869.622 \n",
       "  1510.13,879.525 1511.13,889.466 1512.14,899.442 1513.14,909.449 1514.15,919.486 1515.15,929.548 1516.16,939.633 1517.16,949.737 1518.17,959.856 1519.17,969.987 \n",
       "  1520.17,980.126 1521.18,990.27 1522.18,1000.41 1523.19,1010.56 1524.19,1020.69 1525.2,1030.81 1526.2,1040.92 1527.2,1051.01 1528.21,1061.07 1529.21,1071.11 \n",
       "  1530.22,1081.11 1531.22,1091.08 1532.23,1101 1533.23,1110.88 1534.24,1120.71 1535.24,1130.48 1536.24,1140.19 1537.25,1149.83 1538.25,1159.41 1539.26,1168.91 \n",
       "  1540.26,1178.33 1541.27,1187.66 1542.27,1196.91 1543.27,1206.06 1544.28,1215.11 1545.28,1224.06 1546.29,1232.89 1547.29,1241.61 1548.3,1250.21 1549.3,1258.69 \n",
       "  1550.3,1267.04 1551.31,1275.25 1552.31,1283.32 1553.32,1291.25 1554.32,1299.03 1555.33,1306.65 1556.33,1314.12 1557.34,1321.42 1558.34,1328.55 1559.34,1335.51 \n",
       "  1560.35,1342.3 1561.35,1348.9 1562.36,1355.31 1563.36,1361.54 1564.37,1367.57 1565.37,1373.4 1566.37,1379.03 1567.38,1384.46 1568.38,1389.67 1569.39,1394.68 \n",
       "  1570.39,1399.46 1571.4,1404.03 1572.4,1408.37 1573.41,1412.48 1574.41,1416.37 1575.41,1420.03 1576.42,1423.45 1577.42,1426.63 1578.43,1429.58 1579.43,1432.28 \n",
       "  1580.44,1434.74 1581.44,1436.96 1582.44,1438.93 1583.45,1440.65 1584.45,1442.12 1585.46,1443.34 1586.46,1444.31 1587.47,1445.03 1588.47,1445.5 1589.47,1445.72 \n",
       "  1590.48,1445.68 1591.48,1445.39 1592.49,1444.84 1593.49,1444.05 1594.5,1443 1595.5,1441.7 1596.51,1440.16 1597.51,1438.36 1598.51,1436.32 1599.52,1434.03 \n",
       "  1600.52,1431.49 1601.53,1428.72 1602.53,1425.7 1603.54,1422.45 1604.54,1418.95 1605.54,1415.23 1606.55,1411.27 1607.55,1407.09 1608.56,1402.68 1609.56,1398.05 \n",
       "  1610.57,1393.2 1611.57,1388.13 1612.58,1382.85 1613.58,1377.37 1614.58,1371.67 1615.59,1365.78 1616.59,1359.69 1617.6,1353.41 1618.6,1346.94 1619.61,1340.28 \n",
       "  1620.61,1333.44 1621.61,1326.43 1622.62,1319.25 1623.62,1311.89 1624.63,1304.38 1625.63,1296.71 1626.64,1288.89 1627.64,1280.92 1628.64,1272.8 1629.65,1264.55 \n",
       "  1630.65,1256.16 1631.66,1247.65 1632.66,1239.01 1633.67,1230.25 1634.67,1221.38 1635.68,1212.41 1636.68,1203.33 1637.68,1194.15 1638.69,1184.87 1639.69,1175.51 \n",
       "  1640.7,1166.07 1641.7,1156.54 1642.71,1146.95 1643.71,1137.28 1644.71,1127.55 1645.72,1117.76 1646.72,1107.92 1647.73,1098.03 1648.73,1088.09 1649.74,1078.11 \n",
       "  1650.74,1068.1 1651.74,1058.06 1652.75,1047.98 1653.75,1037.89 1654.76,1027.78 1655.76,1017.65 1656.77,1007.51 1657.77,997.371 1658.78,987.226 1659.78,977.084 \n",
       "  1660.78,966.946 1661.79,956.818 1662.79,946.704 1663.8,936.605 1664.8,926.527 1665.81,916.472 1666.81,906.444 1667.81,896.445 1668.82,886.48 1669.82,876.55 \n",
       "  1670.83,866.659 1671.83,856.809 1672.84,847.004 1673.84,837.245 1674.85,827.536 1675.85,817.879 1676.85,808.276 1677.86,798.729 1678.86,789.241 1679.87,779.814 \n",
       "  1680.87,770.449 1681.88,761.148 1682.88,751.914 1683.88,742.748 1684.89,733.651 1685.89,724.626 1686.9,715.673 1687.9,706.794 1688.91,697.991 1689.91,689.264 \n",
       "  1690.91,680.614 1691.92,672.044 1692.92,663.553 1693.93,655.142 1694.93,646.813 1695.94,638.566 1696.94,630.403 1697.95,622.322 1698.95,614.326 1699.95,606.415 \n",
       "  1700.96,598.588 1701.96,590.847 1702.97,583.192 1703.97,575.623 1704.98,568.141 1705.98,560.744 1706.98,553.435 1707.99,546.212 1708.99,539.075 1710,532.026 \n",
       "  1711,525.062 1712.01,518.186 1713.01,511.395 1714.02,504.691 1715.02,498.072 1716.02,491.54 1717.03,485.092 1718.03,478.729 1719.04,472.451 1720.04,466.257 \n",
       "  1721.05,460.147 1722.05,454.12 1723.05,448.176 1724.06,442.314 1725.06,436.533 1726.07,430.834 1727.07,425.216 1728.08,419.677 1729.08,414.218 1730.08,408.837 \n",
       "  1731.09,403.535 1732.09,398.31 1733.1,393.162 1734.1,388.089 1735.11,383.092 1736.11,378.17 1737.12,373.321 1738.12,368.546 1739.12,363.843 1740.13,359.211 \n",
       "  1741.13,354.651 1742.14,350.16 1743.14,345.739 1744.15,341.386 1745.15,337.101 1746.15,332.883 1747.16,328.731 1748.16,324.644 1749.17,320.622 1750.17,316.663 \n",
       "  1751.18,312.768 1752.18,308.935 1753.18,305.163 1754.19,301.452 1755.19,297.8 1756.2,294.208 1757.2,290.673 1758.21,287.197 1759.21,283.776 1760.22,280.412 \n",
       "  1761.22,277.103 1762.22,273.848 1763.23,270.646 1764.23,267.498 1765.24,264.401 1766.24,261.356 1767.25,258.361 1768.25,255.416 1769.25,252.521 1770.26,249.673 \n",
       "  1771.26,246.873 1772.27,244.12 1773.27,241.414 1774.28,238.752 1775.28,236.136 1776.29,233.564 1777.29,231.035 1778.29,228.549 1779.3,226.105 1780.3,223.703 \n",
       "  1781.31,221.341 1782.31,219.02 1783.32,216.738 1784.32,214.495 1785.32,212.29 1786.33,210.123 1787.33,207.993 1788.34,205.899 1789.34,203.842 1790.35,201.819 \n",
       "  1791.35,199.832 1792.35,197.878 1793.36,195.958 1794.36,194.072 1795.37,192.217 1796.37,190.395 1797.38,188.604 1798.38,186.844 1799.39,185.115 1800.39,183.415 \n",
       "  1801.39,181.745 1802.4,180.104 1803.4,178.491 1804.41,176.907 1805.41,175.349 1806.42,173.819 1807.42,172.315 1808.42,170.838 1809.43,169.386 1810.43,167.959 \n",
       "  1811.44,166.557 1812.44,165.18 1813.45,163.826 1814.45,162.497 1815.46,161.19 1816.46,159.906 1817.46,158.644 1818.47,157.405 1819.47,156.187 1820.48,154.991 \n",
       "  1821.48,153.815 1822.49,152.66 1823.49,151.525 1824.49,150.409 1825.5,149.314 1826.5,148.237 1827.51,147.18 1828.51,146.14 1829.52,145.119 1830.52,144.116 \n",
       "  1831.52,143.131 1832.53,142.162 1833.53,141.211 1834.54,140.276 1835.54,139.358 1836.55,138.456 1837.55,137.569 1838.56,136.698 1839.56,135.843 1840.56,135.002 \n",
       "  1841.57,134.176 1842.57,133.365 1843.58,132.568 1844.58,131.784 1845.59,131.015 1846.59,130.259 1847.59,129.516 1848.6,128.786 1849.6,128.07 1850.61,127.365 \n",
       "  1851.61,126.673 1852.62,125.994 1853.62,125.326 1854.63,124.669 1855.63,124.025 1856.63,123.391 1857.64,122.769 1858.64,122.158 1859.65,121.557 1860.65,120.967 \n",
       "  1861.66,120.388 1862.66,119.818 1863.66,119.259 1864.67,118.709 1865.67,118.169 1866.68,117.639 1867.68,117.117 1868.69,116.605 1869.69,116.102 1870.69,115.608 \n",
       "  1871.7,115.123 1872.7,114.646 1873.71,114.177 1874.71,113.717 1875.72,113.264 1876.72,112.82 1877.73,112.383 1878.73,111.954 1879.73,111.533 1880.74,111.119 \n",
       "  1881.74,110.713 1882.75,110.313 1883.75,109.92 1884.76,109.535 1885.76,109.156 1886.76,108.784 1887.77,108.418 1888.77,108.059 1889.78,107.706 1890.78,107.359 \n",
       "  1891.79,107.019 1892.79,106.684 1893.79,106.355 1894.8,106.032 1895.8,105.715 1896.81,105.403 1897.81,105.097 1898.82,104.796 1899.82,104.501 1900.83,104.21 \n",
       "  1901.83,103.925 1902.83,103.645 1903.84,103.369 1904.84,103.099 1905.85,102.833 1906.85,102.572 1907.86,102.316 1908.86,102.064 1909.86,101.816 1910.87,101.573 \n",
       "  1911.87,101.334 1912.88,101.099 1913.88,100.868 1914.89,100.642 1915.89,100.419 1916.9,100.201 1917.9,99.9858 1918.9,99.7748 1919.91,99.5674 1920.91,99.3637 \n",
       "  1921.92,99.1636 1922.92,98.967 1923.93,98.7739 1924.93,98.5841 1925.93,98.3977 1926.94,98.2146 1927.94,98.0346 1928.95,97.8579 1929.95,97.6842 1930.96,97.5136 \n",
       "  1931.96,97.346 1932.96,97.1813 1933.97,97.0196 1934.97,96.8607 1935.98,96.7045 1936.98,96.5511 1937.99,96.4004 1938.99,96.2524 1940,96.107 1941,95.9641 \n",
       "  1942,95.8237 1943.01,95.6858 1944.01,95.5503 1945.02,95.4172 1946.02,95.2864 1947.03,95.158 1948.03,95.0318 1949.03,94.9078 1950.04,94.7859 1951.04,94.6663 \n",
       "  1952.05,94.5487 1953.05,94.4332 1954.06,94.3197 1955.06,94.2083 1956.07,94.0987 1957.07,93.9911 1958.07,93.8854 1959.08,93.7816 1960.08,93.6796 1961.09,93.5793 \n",
       "  1962.09,93.4809 1963.1,93.3841 1964.1,93.2891 1965.1,93.1957 1966.11,93.104 1967.11,93.0139 1968.12,92.9254 1969.12,92.8384 1970.13,92.7529 1971.13,92.669 \n",
       "  1972.13,92.5865 1973.14,92.5055 1974.14,92.4259 1975.15,92.3477 1976.15,92.2709 1977.16,92.1954 1978.16,92.1213 1979.17,92.0484 1980.17,91.9769 1981.17,91.9065 \n",
       "  1982.18,91.8375 1983.18,91.7696 1984.19,91.703 1985.19,91.6375 1986.2,91.5731 1987.2,91.5099 1988.2,91.4478 1989.21,91.3868 1990.21,91.3269 1991.22,91.268 \n",
       "  1992.22,91.2101 1993.23,91.1533 1994.23,91.0975 1995.23,91.0426 1996.24,90.9887 1997.24,90.9358 1998.25,90.8838 1999.25,90.8327 2000.26,90.7825 2001.26,90.7332 \n",
       "  2002.27,90.6847 2003.27,90.6371 2004.27,90.5903 2005.28,90.5444 2006.28,90.4993 2007.29,90.4549 2008.29,90.4114 2009.3,90.3686 2010.3,90.3265 2011.3,90.2852 \n",
       "  2012.31,90.2446 2013.31,90.2048 2014.32,90.1656 2015.32,90.1271 2016.33,90.0893 2017.33,90.0522 2018.34,90.0157 2019.34,89.9799 2020.34,89.9447 2021.35,89.9101 \n",
       "  2022.35,89.8761 2023.36,89.8427 2024.36,89.8099 2025.37,89.7777 2026.37,89.746 2027.37,89.7149 2028.38,89.6843 2029.38,89.6543 2030.39,89.6248 2031.39,89.5959 \n",
       "  2032.4,89.5674 2033.4,89.5394 2034.4,89.512 2035.41,89.485 2036.41,89.4585 2037.42,89.4324 2038.42,89.4068 2039.43,89.3817 2040.43,89.357 2041.44,89.3327 \n",
       "  2042.44,89.3089 2043.44,89.2854 2044.45,89.2624 2045.45,89.2398 2046.46,89.2176 2047.46,89.1958 2048.47,89.1744 2049.47,89.1533 2050.47,89.1326 2051.48,89.1123 \n",
       "  2052.48,89.0923 2053.49,89.0727 2054.49,89.0534 2055.5,89.0345 2056.5,89.0159 2057.51,88.9976 2058.51,88.9797 2059.51,88.9621 2060.52,88.9447 2061.52,88.9277 \n",
       "  2062.53,88.911 2063.53,88.8946 2064.54,88.8784 2065.54,88.8626 2066.54,88.847 2067.55,88.8317 2068.55,88.8166 2069.56,88.8019 2070.56,88.7874 2071.57,88.7731 \n",
       "  2072.57,88.7591 2073.57,88.7453 2074.58,88.7318 2075.58,88.7185 2076.59,88.7055 2077.59,88.6927 2078.6,88.6801 2079.6,88.6677 2080.61,88.6556 2081.61,88.6436 \n",
       "  2082.61,88.6319 2083.62,88.6204 2084.62,88.609 2085.63,88.5979 2086.63,88.587 2087.64,88.5763 2088.64,88.5657 2089.64,88.5553 2090.65,88.5452 2091.65,88.5352 \n",
       "  2092.66,88.5253 2093.66,88.5157 2094.67,88.5062 2095.67,88.4969 2096.68,88.4877 2097.68,88.4788 2098.68,88.4699 2099.69,88.4612 2100.69,88.4527 2101.7,88.4443 \n",
       "  2102.7,88.4361 2103.71,88.428 2104.71,88.4201 2105.71,88.4123 2106.72,88.4046 2107.72,88.3971 2108.73,88.3897 2109.73,88.3824 2110.74,88.3753 2111.74,88.3683 \n",
       "  2112.74,88.3614 2113.75,88.3546 2114.75,88.348 2115.76,88.3414 2116.76,88.335 2117.77,88.3287 2118.77,88.3225 2119.78,88.3164 2120.78,88.3104 2121.78,88.3046 \n",
       "  2122.79,88.2988 2123.79,88.2931 2124.8,88.2875 2125.8,88.2821 2126.81,88.2767 2127.81,88.2714 2128.81,88.2662 2129.82,88.2611 2130.82,88.2561 2131.83,88.2512 \n",
       "  2132.83,88.2464 2133.84,88.2416 2134.84,88.2369 2135.84,88.2324 2136.85,88.2279 2137.85,88.2234 2138.86,88.2191 2139.86,88.2148 2140.87,88.2106 2141.87,88.2065 \n",
       "  2142.88,88.2025 2143.88,88.1985 2144.88,88.1946 2145.89,88.1907 2146.89,88.187 2147.9,88.1833 2148.9,88.1796 2149.91,88.176 2150.91,88.1725 2151.91,88.1691 \n",
       "  2152.92,88.1657 2153.92,88.1624 2154.93,88.1591 2155.93,88.1559 2156.94,88.1527 2157.94,88.1496 2158.95,88.1466 2159.95,88.1436 2160.95,88.1406 2161.96,88.1377 \n",
       "  2162.96,88.1349 2163.97,88.1321 2164.97,88.1294 2165.98,88.1267 2166.98,88.124 2167.98,88.1214 2168.99,88.1189 2169.99,88.1164 2171,88.1139 2172,88.1115 \n",
       "  2173.01,88.1091 2174.01,88.1068 2175.01,88.1045 2176.02,88.1022 2177.02,88.1 2178.03,88.0978 2179.03,88.0957 2180.04,88.0936 2181.04,88.0915 2182.05,88.0895 \n",
       "  2183.05,88.0875 2184.05,88.0855 2185.06,88.0836 2186.06,88.0817 2187.07,88.0799 2188.07,88.078 2189.08,88.0762 2190.08,88.0745 2191.08,88.0728 2192.09,88.0711 \n",
       "  2193.09,88.0694 2194.1,88.0678 2195.1,88.0661 2196.11,88.0646 2197.11,88.063 2198.12,88.0615 2199.12,88.06 2200.12,88.0585 2201.13,88.0571 2202.13,88.0556 \n",
       "  2203.14,88.0542 2204.14,88.0529 2205.15,88.0515 2206.15,88.0502 2207.15,88.0489 2208.16,88.0476 2209.16,88.0464 2210.17,88.0451 2211.17,88.0439 2212.18,88.0427 \n",
       "  2213.18,88.0415 2214.18,88.0404 2215.19,88.0393 2216.19,88.0382 2217.2,88.0371 2218.2,88.036 2219.21,88.0349 2220.21,88.0339 2221.22,88.0329 2222.22,88.0319 \n",
       "  2223.22,88.0309 2224.23,88.03 2225.23,88.029 2226.24,88.0281 2227.24,88.0272 2228.25,88.0263 2229.25,88.0254 2230.25,88.0245 2231.26,88.0237 2232.26,88.0228 \n",
       "  2233.27,88.022 2234.27,88.0212 2235.28,88.0204 2236.28,88.0196 2237.28,88.0189 2238.29,88.0181 2239.29,88.0174 2240.3,88.0167 2241.3,88.0159 2242.31,88.0152 \n",
       "  2243.31,88.0146 2244.32,88.0139 2245.32,88.0132 2246.32,88.0126 2247.33,88.0119 2248.33,88.0113 2249.34,88.0107 2250.34,88.0101 2251.35,88.0095 2252.35,88.0089 \n",
       "  2253.35,88.0083 2254.36,88.0077 2255.36,88.0072 2256.37,88.0066 2257.37,88.0061 2258.38,88.0056 2259.38,88.0051 2260.39,88.0046 2261.39,88.0041 2262.39,88.0036 \n",
       "  2263.4,88.0031 2264.4,88.0026 2265.41,88.0021 2266.41,88.0017 2267.42,88.0012 2268.42,88.0008 2269.42,88.0004 2270.43,87.9999 2271.43,87.9995 2272.44,87.9991 \n",
       "  2273.44,87.9987 2274.45,87.9983 2275.45,87.9979 2276.45,87.9975 2277.46,87.9972 2278.46,87.9968 2279.47,87.9964 2280.47,87.9961 2281.48,87.9957 2282.48,87.9954 \n",
       "  2283.49,87.995 2284.49,87.9947 2285.49,87.9944 2286.5,87.9941 2287.5,87.9937 2288.51,87.9934 2289.51,87.9931 2290.52,87.9928 2291.52,87.9925 2292.52,87.9922 \n",
       "  \n",
       "  \"/>\n",
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      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = 3\n",
    "N = 2000\n",
    "xmax = 10.0\n",
    "xmin = -10.0\n",
    "xvec = range(xmin,xmax,length=N)\n",
    "V1(x) =  V0*exp(-(x-x0)^2)\n",
    "mat_H1 = make_H1dp(N,xmax,xmin,V1) \n",
    "energy1,mat_v1 = eigen(mat_H1)\n",
    "ψ1 = mat_v1[:,1]\n",
    "println(energy1[1])\n",
    "using Plots\n",
    "plot(xvec,ψ1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "次に、$\\psi_2(x)$は"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.140350685252034\n"
     ]
    },
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       "  726.732,127.365 727.737,128.07 728.741,128.786 729.745,129.516 730.75,130.259 731.754,131.015 732.758,131.784 733.763,132.568 734.767,133.365 735.771,134.176 \n",
       "  736.776,135.002 737.78,135.843 738.785,136.698 739.789,137.569 740.793,138.456 741.798,139.358 742.802,140.276 743.806,141.211 744.811,142.162 745.815,143.131 \n",
       "  746.819,144.116 747.824,145.119 748.828,146.14 749.832,147.18 750.837,148.237 751.841,149.314 752.846,150.409 753.85,151.525 754.854,152.66 755.859,153.815 \n",
       "  756.863,154.991 757.867,156.187 758.872,157.405 759.876,158.644 760.88,159.906 761.885,161.19 762.889,162.497 763.893,163.826 764.898,165.18 765.902,166.557 \n",
       "  766.907,167.959 767.911,169.386 768.915,170.838 769.92,172.315 770.924,173.819 771.928,175.349 772.933,176.907 773.937,178.491 774.941,180.104 775.946,181.745 \n",
       "  776.95,183.415 777.954,185.115 778.959,186.844 779.963,188.604 780.968,190.395 781.972,192.217 782.976,194.072 783.981,195.958 784.985,197.878 785.989,199.832 \n",
       "  786.994,201.819 787.998,203.842 789.002,205.899 790.007,207.993 791.011,210.123 792.015,212.29 793.02,214.495 794.024,216.738 795.029,219.02 796.033,221.341 \n",
       "  797.037,223.703 798.042,226.105 799.046,228.549 800.05,231.035 801.055,233.564 802.059,236.136 803.063,238.752 804.068,241.414 805.072,244.12 806.076,246.873 \n",
       "  807.081,249.673 808.085,252.521 809.09,255.416 810.094,258.361 811.098,261.356 812.103,264.401 813.107,267.498 814.111,270.646 815.116,273.848 816.12,277.103 \n",
       "  817.124,280.412 818.129,283.776 819.133,287.197 820.137,290.673 821.142,294.208 822.146,297.8 823.151,301.452 824.155,305.163 825.159,308.935 826.164,312.768 \n",
       "  827.168,316.663 828.172,320.622 829.177,324.644 830.181,328.731 831.185,332.883 832.19,337.101 833.194,341.386 834.198,345.739 835.203,350.16 836.207,354.651 \n",
       "  837.212,359.211 838.216,363.843 839.22,368.546 840.225,373.321 841.229,378.17 842.233,383.092 843.238,388.089 844.242,393.162 845.246,398.31 846.251,403.535 \n",
       "  847.255,408.837 848.259,414.218 849.264,419.677 850.268,425.216 851.273,430.834 852.277,436.533 853.281,442.314 854.286,448.176 855.29,454.12 856.294,460.147 \n",
       "  857.299,466.257 858.303,472.451 859.307,478.729 860.312,485.092 861.316,491.54 862.32,498.072 863.325,504.691 864.329,511.395 865.334,518.186 866.338,525.062 \n",
       "  867.342,532.026 868.347,539.075 869.351,546.212 870.355,553.435 871.36,560.744 872.364,568.141 873.368,575.623 874.373,583.192 875.377,590.847 876.381,598.588 \n",
       "  877.386,606.415 878.39,614.326 879.395,622.322 880.399,630.403 881.403,638.566 882.408,646.813 883.412,655.142 884.416,663.553 885.421,672.044 886.425,680.614 \n",
       "  887.429,689.264 888.434,697.991 889.438,706.794 890.442,715.673 891.447,724.626 892.451,733.651 893.456,742.748 894.46,751.914 895.464,761.148 896.469,770.449 \n",
       "  897.473,779.814 898.477,789.241 899.482,798.729 900.486,808.276 901.49,817.879 902.495,827.536 903.499,837.245 904.503,847.004 905.508,856.809 906.512,866.659 \n",
       "  907.517,876.55 908.521,886.48 909.525,896.445 910.53,906.444 911.534,916.472 912.538,926.527 913.543,936.605 914.547,946.704 915.551,956.818 916.556,966.946 \n",
       "  917.56,977.084 918.564,987.226 919.569,997.371 920.573,1007.51 921.578,1017.65 922.582,1027.78 923.586,1037.89 924.591,1047.98 925.595,1058.06 926.599,1068.1 \n",
       "  927.604,1078.11 928.608,1088.09 929.612,1098.03 930.617,1107.92 931.621,1117.76 932.625,1127.55 933.63,1137.28 934.634,1146.95 935.639,1156.54 936.643,1166.07 \n",
       "  937.647,1175.51 938.652,1184.87 939.656,1194.15 940.66,1203.33 941.665,1212.41 942.669,1221.38 943.673,1230.25 944.678,1239.01 945.682,1247.65 946.686,1256.16 \n",
       "  947.691,1264.55 948.695,1272.8 949.7,1280.92 950.704,1288.89 951.708,1296.71 952.713,1304.38 953.717,1311.89 954.721,1319.25 955.726,1326.43 956.73,1333.44 \n",
       "  957.734,1340.28 958.739,1346.94 959.743,1353.41 960.747,1359.69 961.752,1365.78 962.756,1371.67 963.76,1377.37 964.765,1382.85 965.769,1388.13 966.774,1393.2 \n",
       "  967.778,1398.05 968.782,1402.68 969.787,1407.09 970.791,1411.27 971.795,1415.23 972.8,1418.95 973.804,1422.45 974.808,1425.7 975.813,1428.72 976.817,1431.49 \n",
       "  977.821,1434.03 978.826,1436.32 979.83,1438.36 980.835,1440.16 981.839,1441.7 982.843,1443 983.848,1444.05 984.852,1444.84 985.856,1445.39 986.861,1445.68 \n",
       "  987.865,1445.72 988.869,1445.5 989.874,1445.03 990.878,1444.31 991.882,1443.34 992.887,1442.12 993.891,1440.65 994.896,1438.93 995.9,1436.96 996.904,1434.74 \n",
       "  997.909,1432.28 998.913,1429.58 999.917,1426.63 1000.92,1423.45 1001.93,1420.03 1002.93,1416.37 1003.93,1412.48 1004.94,1408.37 1005.94,1404.03 1006.95,1399.46 \n",
       "  1007.95,1394.68 1008.96,1389.67 1009.96,1384.46 1010.97,1379.03 1011.97,1373.4 1012.97,1367.57 1013.98,1361.54 1014.98,1355.31 1015.99,1348.9 1016.99,1342.3 \n",
       "  1018,1335.51 1019,1328.55 1020,1321.42 1021.01,1314.12 1022.01,1306.65 1023.02,1299.03 1024.02,1291.25 1025.03,1283.32 1026.03,1275.25 1027.03,1267.04 \n",
       "  1028.04,1258.69 1029.04,1250.21 1030.05,1241.61 1031.05,1232.89 1032.06,1224.06 1033.06,1215.11 1034.07,1206.06 1035.07,1196.91 1036.07,1187.66 1037.08,1178.33 \n",
       "  1038.08,1168.91 1039.09,1159.41 1040.09,1149.83 1041.1,1140.19 1042.1,1130.48 1043.1,1120.71 1044.11,1110.88 1045.11,1101 1046.12,1091.08 1047.12,1081.11 \n",
       "  1048.13,1071.11 1049.13,1061.07 1050.14,1051.01 1051.14,1040.92 1052.14,1030.81 1053.15,1020.69 1054.15,1010.56 1055.16,1000.41 1056.16,990.27 1057.17,980.126 \n",
       "  1058.17,969.987 1059.17,959.856 1060.18,949.737 1061.18,939.633 1062.19,929.548 1063.19,919.486 1064.2,909.449 1065.2,899.442 1066.2,889.466 1067.21,879.525 \n",
       "  1068.21,869.622 1069.22,859.759 1070.22,849.941 1071.23,840.168 1072.23,830.444 1073.24,820.771 1074.24,811.151 1075.24,801.587 1076.25,792.081 1077.25,782.635 \n",
       "  1078.26,773.251 1079.26,763.931 1080.27,754.677 1081.27,745.49 1082.27,736.373 1083.28,727.326 1084.28,718.351 1085.29,709.45 1086.29,700.624 1087.3,691.874 \n",
       "  1088.3,683.201 1089.31,674.606 1090.31,666.091 1091.31,657.657 1092.32,649.303 1093.32,641.032 1094.33,632.843 1095.33,624.738 1096.34,616.716 1097.34,608.779 \n",
       "  1098.34,600.927 1099.35,593.161 1100.35,585.48 1101.36,577.885 1102.36,570.376 1103.37,562.954 1104.37,555.618 1105.37,548.369 1106.38,541.207 1107.38,534.131 \n",
       "  1108.39,527.142 1109.39,520.24 1110.4,513.423 1111.4,506.693 1112.41,500.049 1113.41,493.49 1114.41,487.017 1115.42,480.629 1116.42,474.326 1117.43,468.106 \n",
       "  1118.43,461.971 1119.44,455.919 1120.44,449.95 1121.44,444.064 1122.45,438.259 1123.45,432.535 1124.46,426.893 1125.46,421.33 1126.47,415.847 1127.47,410.443 \n",
       "  1128.48,405.118 1129.48,399.869 1130.48,394.698 1131.49,389.603 1132.49,384.584 1133.5,379.639 1134.5,374.768 1135.51,369.971 1136.51,365.246 1137.51,360.593 \n",
       "  1138.52,356.011 1139.52,351.5 1140.53,347.058 1141.53,342.684 1142.54,338.379 1143.54,334.141 1144.54,329.969 1145.55,325.863 1146.55,321.822 1147.56,317.844 \n",
       "  1148.56,313.93 1149.57,310.078 1150.57,306.288 1151.58,302.559 1152.58,298.889 1153.58,295.279 1154.59,291.728 1155.59,288.234 1156.6,284.797 1157.6,281.415 \n",
       "  1158.61,278.09 1159.61,274.819 1160.61,271.601 1161.62,268.437 1162.62,265.325 1163.63,262.264 1164.63,259.254 1165.64,256.295 1166.64,253.384 1167.64,250.522 \n",
       "  1168.65,247.708 1169.65,244.941 1170.66,242.221 1171.66,239.546 1172.67,236.916 1173.67,234.331 1174.68,231.789 1175.68,229.29 1176.68,226.834 1177.69,224.419 \n",
       "  1178.69,222.045 1179.7,219.712 1180.7,217.418 1181.71,215.163 1182.71,212.947 1183.71,210.769 1184.72,208.628 1185.72,206.524 1186.73,204.455 1187.73,202.422 \n",
       "  1188.74,200.424 1189.74,198.461 1190.75,196.531 1191.75,194.634 1192.75,192.77 1193.76,190.939 1194.76,189.138 1195.77,187.369 1196.77,185.631 1197.78,183.922 \n",
       "  1198.78,182.243 1199.78,180.593 1200.79,178.972 1201.79,177.379 1202.8,175.814 1203.8,174.275 1204.81,172.764 1205.81,171.278 1206.81,169.819 1207.82,168.384 \n",
       "  1208.82,166.975 1209.83,165.591 1210.83,164.23 1211.84,162.893 1212.84,161.579 1213.85,160.289 1214.85,159.021 1215.85,157.775 1216.86,156.55 1217.86,155.347 \n",
       "  1218.87,154.165 1219.87,153.004 1220.88,151.863 1221.88,150.742 1222.88,149.64 1223.89,148.558 1224.89,147.495 1225.9,146.45 1226.9,145.424 1227.91,144.415 \n",
       "  1228.91,143.425 1229.92,142.451 1230.92,141.495 1231.92,140.555 1232.93,139.632 1233.93,138.725 1234.94,137.834 1235.94,136.958 1236.95,136.098 1237.95,135.253 \n",
       "  1238.95,134.422 1239.96,133.607 1240.96,132.805 1241.97,132.018 1242.97,131.244 1243.98,130.484 1244.98,129.738 1245.98,129.004 1246.99,128.283 1247.99,127.575 \n",
       "  1249,126.88 1250,126.196 1251.01,125.525 1252.01,124.865 1253.02,124.217 1254.02,123.58 1255.02,122.955 1256.03,122.34 1257.03,121.736 1258.04,121.143 \n",
       "  1259.04,120.561 1260.05,119.988 1261.05,119.426 1262.05,118.873 1263.06,118.33 1264.06,117.797 1265.07,117.273 1266.07,116.758 1267.08,116.252 1268.08,115.756 \n",
       "  1269.08,115.267 1270.09,114.788 1271.09,114.317 1272.1,113.854 1273.1,113.399 1274.11,112.952 1275.11,112.514 1276.12,112.082 1277.12,111.659 1278.12,111.243 \n",
       "  1279.13,110.834 1280.13,110.432 1281.14,110.037 1282.14,109.65 1283.15,109.269 1284.15,108.895 1285.15,108.527 1286.16,108.166 1287.16,107.811 1288.17,107.463 \n",
       "  1289.17,107.12 1290.18,106.784 1291.18,106.453 1292.19,106.129 1293.19,105.81 1294.19,105.496 1295.2,105.188 1296.2,104.886 1297.21,104.589 1298.21,104.297 \n",
       "  1299.22,104.01 1300.22,103.728 1301.22,103.451 1302.23,103.179 1303.23,102.912 1304.24,102.65 1305.24,102.392 1306.25,102.139 1307.25,101.89 1308.25,101.645 \n",
       "  1309.26,101.405 1310.26,101.169 1311.27,100.937 1312.27,100.709 1313.28,100.486 1314.28,100.266 1315.29,100.05 1316.29,99.8377 1317.29,99.6293 1318.3,99.4245 \n",
       "  1319.3,99.2233 1320.31,99.0256 1321.31,98.8315 1322.32,98.6407 1323.32,98.4533 1324.32,98.2692 1325.33,98.0883 1326.33,97.9106 1327.34,97.736 1328.34,97.5645 \n",
       "  1329.35,97.396 1330.35,97.2304 1331.36,97.0678 1332.36,96.908 1333.36,96.7511 1334.37,96.5969 1335.37,96.4454 1336.38,96.2965 1337.38,96.1503 1338.39,96.0067 \n",
       "  1339.39,95.8655 1340.39,95.7269 1341.4,95.5907 1342.4,95.4569 1343.41,95.3254 1344.41,95.1963 1345.42,95.0694 1346.42,94.9447 1347.42,94.8223 1348.43,94.702 \n",
       "  1349.43,94.5838 1350.44,94.4676 1351.44,94.3536 1352.45,94.2415 1353.45,94.1314 1354.46,94.0232 1355.46,93.9169 1356.46,93.8125 1357.47,93.71 1358.47,93.6092 \n",
       "  1359.48,93.5102 1360.48,93.413 1361.49,93.3174 1362.49,93.2236 1363.49,93.1313 1364.5,93.0408 1365.5,92.9518 1366.51,92.8643 1367.51,92.7784 1368.52,92.694 \n",
       "  1369.52,92.6111 1370.53,92.5297 1371.53,92.4496 1372.53,92.371 1373.54,92.2938 1374.54,92.2179 1375.55,92.1434 1376.55,92.0701 1377.56,91.9982 1378.56,91.9275 \n",
       "  1379.56,91.8581 1380.57,91.7898 1381.57,91.7228 1382.58,91.657 1383.58,91.5923 1384.59,91.5288 1385.59,91.4663 1386.59,91.405 1387.6,91.3447 1388.6,91.2855 \n",
       "  1389.61,91.2274 1390.61,91.1702 1391.62,91.1141 1392.62,91.059 1393.63,91.0048 1394.63,90.9516 1395.63,90.8993 1396.64,90.8479 1397.64,90.7974 1398.65,90.7479 \n",
       "  1399.65,90.6991 1400.66,90.6513 1401.66,90.6043 1402.66,90.5581 1403.67,90.5127 1404.67,90.4681 1405.68,90.4244 1406.68,90.3813 1407.69,90.3391 1408.69,90.2975 \n",
       "  1409.69,90.2567 1410.7,90.2167 1411.7,90.1773 1412.71,90.1386 1413.71,90.1006 1414.72,90.0633 1415.72,90.0266 1416.73,89.9906 1417.73,89.9552 1418.73,89.9204 \n",
       "  1419.74,89.8862 1420.74,89.8526 1421.75,89.8197 1422.75,89.7873 1423.76,89.7554 1424.76,89.7242 1425.76,89.6935 1426.77,89.6633 1427.77,89.6336 1428.78,89.6045 \n",
       "  1429.78,89.5759 1430.79,89.5478 1431.79,89.5201 1432.8,89.493 1433.8,89.4664 1434.8,89.4402 1435.81,89.4144 1436.81,89.3892 1437.82,89.3643 1438.82,89.3399 \n",
       "  1439.83,89.316 1440.83,89.2924 1441.83,89.2693 1442.84,89.2466 1443.84,89.2242 1444.85,89.2023 1445.85,89.1808 1446.86,89.1596 1447.86,89.1388 1448.86,89.1184 \n",
       "  1449.87,89.0983 1450.87,89.0786 1451.88,89.0592 1452.88,89.0402 1453.89,89.0215 1454.89,89.0031 1455.9,88.985 1456.9,88.9673 1457.9,88.9499 1458.91,88.9328 \n",
       "  1459.91,88.916 1460.92,88.8995 1461.92,88.8832 1462.93,88.8673 1463.93,88.8516 1464.93,88.8362 1465.94,88.8211 1466.94,88.8063 1467.95,88.7917 1468.95,88.7774 \n",
       "  1469.96,88.7633 1470.96,88.7494 1471.97,88.7358 1472.97,88.7225 1473.97,88.7094 1474.98,88.6965 1475.98,88.6838 1476.99,88.6714 1477.99,88.6592 1479,88.6472 \n",
       "  1480,88.6354 1481,88.6238 1482.01,88.6124 1483.01,88.6012 1484.02,88.5903 1485.02,88.5795 1486.03,88.5689 1487.03,88.5584 1488.03,88.5482 1489.04,88.5382 \n",
       "  1490.04,88.5283 1491.05,88.5186 1492.05,88.509 1493.06,88.4997 1494.06,88.4905 1495.07,88.4814 1496.07,88.4726 1497.07,88.4638 1498.08,88.4553 1499.08,88.4468 \n",
       "  1500.09,88.4386 1501.09,88.4304 1502.1,88.4225 1503.1,88.4146 1504.1,88.4069 1505.11,88.3993 1506.11,88.3919 1507.12,88.3846 1508.12,88.3774 1509.13,88.3704 \n",
       "  1510.13,88.3634 1511.13,88.3566 1512.14,88.3499 1513.14,88.3434 1514.15,88.3369 1515.15,88.3306 1516.16,88.3243 1517.16,88.3182 1518.17,88.3122 1519.17,88.3063 \n",
       "  1520.17,88.3005 1521.18,88.2948 1522.18,88.2892 1523.19,88.2837 1524.19,88.2783 1525.2,88.273 1526.2,88.2678 1527.2,88.2626 1528.21,88.2576 1529.21,88.2527 \n",
       "  1530.22,88.2478 1531.22,88.243 1532.23,88.2383 1533.23,88.2337 1534.24,88.2292 1535.24,88.2248 1536.24,88.2204 1537.25,88.2161 1538.25,88.2119 1539.26,88.2077 \n",
       "  1540.26,88.2037 1541.27,88.1997 1542.27,88.1957 1543.27,88.1919 1544.28,88.1881 1545.28,88.1844 1546.29,88.1807 1547.29,88.1771 1548.3,88.1736 1549.3,88.1701 \n",
       "  1550.3,88.1667 1551.31,88.1633 1552.31,88.1601 1553.32,88.1568 1554.32,88.1536 1555.33,88.1505 1556.33,88.1475 1557.34,88.1445 1558.34,88.1415 1559.34,88.1386 \n",
       "  1560.35,88.1357 1561.35,88.1329 1562.36,88.1302 1563.36,88.1275 1564.37,88.1248 1565.37,88.1222 1566.37,88.1196 1567.38,88.1171 1568.38,88.1146 1569.39,88.1122 \n",
       "  1570.39,88.1098 1571.4,88.1075 1572.4,88.1051 1573.41,88.1029 1574.41,88.1006 1575.41,88.0985 1576.42,88.0963 1577.42,88.0942 1578.43,88.0921 1579.43,88.0901 \n",
       "  1580.44,88.0881 1581.44,88.0861 1582.44,88.0842 1583.45,88.0823 1584.45,88.0804 1585.46,88.0786 1586.46,88.0768 1587.47,88.075 1588.47,88.0733 1589.47,88.0716 \n",
       "  1590.48,88.0699 1591.48,88.0682 1592.49,88.0666 1593.49,88.065 1594.5,88.0635 1595.5,88.0619 1596.51,88.0604 1597.51,88.0589 1598.51,88.0575 1599.52,88.0561 \n",
       "  1600.52,88.0547 1601.53,88.0533 1602.53,88.0519 1603.54,88.0506 1604.54,88.0493 1605.54,88.048 1606.55,88.0467 1607.55,88.0455 1608.56,88.0443 1609.56,88.0431 \n",
       "  1610.57,88.0419 1611.57,88.0407 1612.58,88.0396 1613.58,88.0385 1614.58,88.0374 1615.59,88.0363 1616.59,88.0353 1617.6,88.0342 1618.6,88.0332 1619.61,88.0322 \n",
       "  1620.61,88.0312 1621.61,88.0302 1622.62,88.0293 1623.62,88.0284 1624.63,88.0274 1625.63,88.0265 1626.64,88.0257 1627.64,88.0248 1628.64,88.0239 1629.65,88.0231 \n",
       "  1630.65,88.0223 1631.66,88.0214 1632.66,88.0207 1633.67,88.0199 1634.67,88.0191 1635.68,88.0183 1636.68,88.0176 1637.68,88.0169 1638.69,88.0162 1639.69,88.0155 \n",
       "  1640.7,88.0148 1641.7,88.0141 1642.71,88.0134 1643.71,88.0128 1644.71,88.0121 1645.72,88.0115 1646.72,88.0109 1647.73,88.0103 1648.73,88.0097 1649.74,88.0091 \n",
       "  1650.74,88.0085 1651.74,88.0079 1652.75,88.0074 1653.75,88.0068 1654.76,88.0063 1655.76,88.0057 1656.77,88.0052 1657.77,88.0047 1658.78,88.0042 1659.78,88.0037 \n",
       "  1660.78,88.0032 1661.79,88.0028 1662.79,88.0023 1663.8,88.0018 1664.8,88.0014 1665.81,88.0009 1666.81,88.0005 1667.81,88.0001 1668.82,87.9996 1669.82,87.9992 \n",
       "  1670.83,87.9988 1671.83,87.9984 1672.84,87.998 1673.84,87.9976 1674.85,87.9973 1675.85,87.9969 1676.85,87.9965 1677.86,87.9962 1678.86,87.9958 1679.87,87.9955 \n",
       "  1680.87,87.9951 1681.88,87.9948 1682.88,87.9945 1683.88,87.9941 1684.89,87.9938 1685.89,87.9935 1686.9,87.9932 1687.9,87.9929 1688.91,87.9926 1689.91,87.9923 \n",
       "  1690.91,87.992 1691.92,87.9918 1692.92,87.9915 1693.93,87.9912 1694.93,87.991 1695.94,87.9907 1696.94,87.9904 1697.95,87.9902 1698.95,87.9899 1699.95,87.9897 \n",
       "  1700.96,87.9895 1701.96,87.9892 1702.97,87.989 1703.97,87.9888 1704.98,87.9885 1705.98,87.9883 1706.98,87.9881 1707.99,87.9879 1708.99,87.9877 1710,87.9875 \n",
       "  1711,87.9873 1712.01,87.9871 1713.01,87.9869 1714.02,87.9867 1715.02,87.9865 1716.02,87.9863 1717.03,87.9862 1718.03,87.986 1719.04,87.9858 1720.04,87.9856 \n",
       "  1721.05,87.9855 1722.05,87.9853 1723.05,87.9852 1724.06,87.985 1725.06,87.9848 1726.07,87.9847 1727.07,87.9845 1728.08,87.9844 1729.08,87.9842 1730.08,87.9841 \n",
       "  1731.09,87.984 1732.09,87.9838 1733.1,87.9837 1734.1,87.9836 1735.11,87.9834 1736.11,87.9833 1737.12,87.9832 1738.12,87.983 1739.12,87.9829 1740.13,87.9828 \n",
       "  1741.13,87.9827 1742.14,87.9826 1743.14,87.9825 1744.15,87.9823 1745.15,87.9822 1746.15,87.9821 1747.16,87.982 1748.16,87.9819 1749.17,87.9818 1750.17,87.9817 \n",
       "  1751.18,87.9816 1752.18,87.9815 1753.18,87.9814 1754.19,87.9813 1755.19,87.9812 1756.2,87.9812 1757.2,87.9811 1758.21,87.981 1759.21,87.9809 1760.22,87.9808 \n",
       "  1761.22,87.9807 1762.22,87.9806 1763.23,87.9806 1764.23,87.9805 1765.24,87.9804 1766.24,87.9803 1767.25,87.9803 1768.25,87.9802 1769.25,87.9801 1770.26,87.98 \n",
       "  1771.26,87.98 1772.27,87.9799 1773.27,87.9798 1774.28,87.9798 1775.28,87.9797 1776.29,87.9797 1777.29,87.9796 1778.29,87.9795 1779.3,87.9795 1780.3,87.9794 \n",
       "  1781.31,87.9794 1782.31,87.9793 1783.32,87.9792 1784.32,87.9792 1785.32,87.9791 1786.33,87.9791 1787.33,87.979 1788.34,87.979 1789.34,87.9789 1790.35,87.9789 \n",
       "  1791.35,87.9788 1792.35,87.9788 1793.36,87.9787 1794.36,87.9787 1795.37,87.9786 1796.37,87.9786 1797.38,87.9786 1798.38,87.9785 1799.39,87.9785 1800.39,87.9784 \n",
       "  1801.39,87.9784 1802.4,87.9783 1803.4,87.9783 1804.41,87.9783 1805.41,87.9782 1806.42,87.9782 1807.42,87.9782 1808.42,87.9781 1809.43,87.9781 1810.43,87.9781 \n",
       "  1811.44,87.978 1812.44,87.978 1813.45,87.978 1814.45,87.9779 1815.46,87.9779 1816.46,87.9779 1817.46,87.9778 1818.47,87.9778 1819.47,87.9778 1820.48,87.9777 \n",
       "  1821.48,87.9777 1822.49,87.9777 1823.49,87.9777 1824.49,87.9776 1825.5,87.9776 1826.5,87.9776 1827.51,87.9776 1828.51,87.9775 1829.52,87.9775 1830.52,87.9775 \n",
       "  1831.52,87.9775 1832.53,87.9774 1833.53,87.9774 1834.54,87.9774 1835.54,87.9774 1836.55,87.9773 1837.55,87.9773 1838.56,87.9773 1839.56,87.9773 1840.56,87.9773 \n",
       "  1841.57,87.9772 1842.57,87.9772 1843.58,87.9772 1844.58,87.9772 1845.59,87.9772 1846.59,87.9771 1847.59,87.9771 1848.6,87.9771 1849.6,87.9771 1850.61,87.9771 \n",
       "  1851.61,87.9771 1852.62,87.977 1853.62,87.977 1854.63,87.977 1855.63,87.977 1856.63,87.977 1857.64,87.977 1858.64,87.977 1859.65,87.9769 1860.65,87.9769 \n",
       "  1861.66,87.9769 1862.66,87.9769 1863.66,87.9769 1864.67,87.9769 1865.67,87.9769 1866.68,87.9768 1867.68,87.9768 1868.69,87.9768 1869.69,87.9768 1870.69,87.9768 \n",
       "  1871.7,87.9768 1872.7,87.9768 1873.71,87.9768 1874.71,87.9768 1875.72,87.9767 1876.72,87.9767 1877.73,87.9767 1878.73,87.9767 1879.73,87.9767 1880.74,87.9767 \n",
       "  1881.74,87.9767 1882.75,87.9767 1883.75,87.9767 1884.76,87.9767 1885.76,87.9766 1886.76,87.9766 1887.77,87.9766 1888.77,87.9766 1889.78,87.9766 1890.78,87.9766 \n",
       "  1891.79,87.9766 1892.79,87.9766 1893.79,87.9766 1894.8,87.9766 1895.8,87.9766 1896.81,87.9766 1897.81,87.9765 1898.82,87.9765 1899.82,87.9765 1900.83,87.9765 \n",
       "  1901.83,87.9765 1902.83,87.9765 1903.84,87.9765 1904.84,87.9765 1905.85,87.9765 1906.85,87.9765 1907.86,87.9765 1908.86,87.9765 1909.86,87.9765 1910.87,87.9765 \n",
       "  1911.87,87.9765 1912.88,87.9765 1913.88,87.9765 1914.89,87.9764 1915.89,87.9764 1916.9,87.9764 1917.9,87.9764 1918.9,87.9764 1919.91,87.9764 1920.91,87.9764 \n",
       "  1921.92,87.9764 1922.92,87.9764 1923.93,87.9764 1924.93,87.9764 1925.93,87.9764 1926.94,87.9764 1927.94,87.9764 1928.95,87.9764 1929.95,87.9764 1930.96,87.9764 \n",
       "  1931.96,87.9764 1932.96,87.9764 1933.97,87.9764 1934.97,87.9764 1935.98,87.9764 1936.98,87.9764 1937.99,87.9764 1938.99,87.9764 1940,87.9763 1941,87.9763 \n",
       "  1942,87.9763 1943.01,87.9763 1944.01,87.9763 1945.02,87.9763 1946.02,87.9763 1947.03,87.9763 1948.03,87.9763 1949.03,87.9763 1950.04,87.9763 1951.04,87.9763 \n",
       "  1952.05,87.9763 1953.05,87.9763 1954.06,87.9763 1955.06,87.9763 1956.07,87.9763 1957.07,87.9763 1958.07,87.9763 1959.08,87.9763 1960.08,87.9763 1961.09,87.9763 \n",
       "  1962.09,87.9763 1963.1,87.9763 1964.1,87.9763 1965.1,87.9763 1966.11,87.9763 1967.11,87.9763 1968.12,87.9763 1969.12,87.9763 1970.13,87.9763 1971.13,87.9763 \n",
       "  1972.13,87.9763 1973.14,87.9763 1974.14,87.9763 1975.15,87.9763 1976.15,87.9763 1977.16,87.9763 1978.16,87.9763 1979.17,87.9763 1980.17,87.9763 1981.17,87.9763 \n",
       "  1982.18,87.9763 1983.18,87.9763 1984.19,87.9763 1985.19,87.9763 1986.2,87.9763 1987.2,87.9763 1988.2,87.9763 1989.21,87.9763 1990.21,87.9763 1991.22,87.9763 \n",
       "  1992.22,87.9763 1993.23,87.9763 1994.23,87.9763 1995.23,87.9763 1996.24,87.9763 1997.24,87.9763 1998.25,87.9763 1999.25,87.9763 2000.26,87.9763 2001.26,87.9763 \n",
       "  2002.27,87.9763 2003.27,87.9763 2004.27,87.9763 2005.28,87.9763 2006.28,87.9763 2007.29,87.9763 2008.29,87.9763 2009.3,87.9763 2010.3,87.9763 2011.3,87.9763 \n",
       "  2012.31,87.9763 2013.31,87.9763 2014.32,87.9763 2015.32,87.9763 2016.33,87.9763 2017.33,87.9763 2018.34,87.9763 2019.34,87.9763 2020.34,87.9763 2021.35,87.9763 \n",
       "  2022.35,87.9763 2023.36,87.9763 2024.36,87.9763 2025.37,87.9763 2026.37,87.9763 2027.37,87.9763 2028.38,87.9763 2029.38,87.9763 2030.39,87.9763 2031.39,87.9763 \n",
       "  2032.4,87.9763 2033.4,87.9763 2034.4,87.9763 2035.41,87.9763 2036.41,87.9763 2037.42,87.9763 2038.42,87.9763 2039.43,87.9763 2040.43,87.9763 2041.44,87.9763 \n",
       "  2042.44,87.9763 2043.44,87.9763 2044.45,87.9763 2045.45,87.9764 2046.46,87.9764 2047.46,87.9764 2048.47,87.9764 2049.47,87.9764 2050.47,87.9764 2051.48,87.9764 \n",
       "  2052.48,87.9764 2053.49,87.9764 2054.49,87.9764 2055.5,87.9764 2056.5,87.9764 2057.51,87.9764 2058.51,87.9764 2059.51,87.9764 2060.52,87.9764 2061.52,87.9764 \n",
       "  2062.53,87.9764 2063.53,87.9764 2064.54,87.9764 2065.54,87.9764 2066.54,87.9764 2067.55,87.9764 2068.55,87.9764 2069.56,87.9764 2070.56,87.9765 2071.57,87.9765 \n",
       "  2072.57,87.9765 2073.57,87.9765 2074.58,87.9765 2075.58,87.9765 2076.59,87.9765 2077.59,87.9765 2078.6,87.9765 2079.6,87.9765 2080.61,87.9765 2081.61,87.9765 \n",
       "  2082.61,87.9765 2083.62,87.9765 2084.62,87.9765 2085.63,87.9765 2086.63,87.9766 2087.64,87.9766 2088.64,87.9766 2089.64,87.9766 2090.65,87.9766 2091.65,87.9766 \n",
       "  2092.66,87.9766 2093.66,87.9766 2094.67,87.9766 2095.67,87.9766 2096.68,87.9766 2097.68,87.9766 2098.68,87.9766 2099.69,87.9767 2100.69,87.9767 2101.7,87.9767 \n",
       "  2102.7,87.9767 2103.71,87.9767 2104.71,87.9767 2105.71,87.9767 2106.72,87.9767 2107.72,87.9767 2108.73,87.9767 2109.73,87.9768 2110.74,87.9768 2111.74,87.9768 \n",
       "  2112.74,87.9768 2113.75,87.9768 2114.75,87.9768 2115.76,87.9768 2116.76,87.9768 2117.77,87.9769 2118.77,87.9769 2119.78,87.9769 2120.78,87.9769 2121.78,87.9769 \n",
       "  2122.79,87.9769 2123.79,87.9769 2124.8,87.9769 2125.8,87.977 2126.81,87.977 2127.81,87.977 2128.81,87.977 2129.82,87.977 2130.82,87.977 2131.83,87.9771 \n",
       "  2132.83,87.9771 2133.84,87.9771 2134.84,87.9771 2135.84,87.9771 2136.85,87.9771 2137.85,87.9772 2138.86,87.9772 2139.86,87.9772 2140.87,87.9772 2141.87,87.9772 \n",
       "  2142.88,87.9773 2143.88,87.9773 2144.88,87.9773 2145.89,87.9773 2146.89,87.9773 2147.9,87.9774 2148.9,87.9774 2149.91,87.9774 2150.91,87.9774 2151.91,87.9774 \n",
       "  2152.92,87.9775 2153.92,87.9775 2154.93,87.9775 2155.93,87.9775 2156.94,87.9776 2157.94,87.9776 2158.95,87.9776 2159.95,87.9776 2160.95,87.9777 2161.96,87.9777 \n",
       "  2162.96,87.9777 2163.97,87.9778 2164.97,87.9778 2165.98,87.9778 2166.98,87.9779 2167.98,87.9779 2168.99,87.9779 2169.99,87.9779 2171,87.978 2172,87.978 \n",
       "  2173.01,87.978 2174.01,87.9781 2175.01,87.9781 2176.02,87.9781 2177.02,87.9782 2178.03,87.9782 2179.03,87.9783 2180.04,87.9783 2181.04,87.9783 2182.05,87.9784 \n",
       "  2183.05,87.9784 2184.05,87.9785 2185.06,87.9785 2186.06,87.9785 2187.07,87.9786 2188.07,87.9786 2189.08,87.9787 2190.08,87.9787 2191.08,87.9788 2192.09,87.9788 \n",
       "  2193.09,87.9789 2194.1,87.9789 2195.1,87.979 2196.11,87.979 2197.11,87.9791 2198.12,87.9791 2199.12,87.9792 2200.12,87.9792 2201.13,87.9793 2202.13,87.9793 \n",
       "  2203.14,87.9794 2204.14,87.9794 2205.15,87.9795 2206.15,87.9796 2207.15,87.9796 2208.16,87.9797 2209.16,87.9798 2210.17,87.9798 2211.17,87.9799 2212.18,87.98 \n",
       "  2213.18,87.98 2214.18,87.9801 2215.19,87.9802 2216.19,87.9802 2217.2,87.9803 2218.2,87.9804 2219.21,87.9805 2220.21,87.9805 2221.22,87.9806 2222.22,87.9807 \n",
       "  2223.22,87.9808 2224.23,87.9809 2225.23,87.981 2226.24,87.981 2227.24,87.9811 2228.25,87.9812 2229.25,87.9813 2230.25,87.9814 2231.26,87.9815 2232.26,87.9816 \n",
       "  2233.27,87.9817 2234.27,87.9818 2235.28,87.9819 2236.28,87.982 2237.28,87.9821 2238.29,87.9822 2239.29,87.9823 2240.3,87.9824 2241.3,87.9825 2242.31,87.9826 \n",
       "  2243.31,87.9828 2244.32,87.9829 2245.32,87.983 2246.32,87.9831 2247.33,87.9833 2248.33,87.9834 2249.34,87.9835 2250.34,87.9836 2251.35,87.9838 2252.35,87.9839 \n",
       "  2253.35,87.9841 2254.36,87.9842 2255.36,87.9843 2256.37,87.9845 2257.37,87.9846 2258.38,87.9848 2259.38,87.9849 2260.39,87.9851 2261.39,87.9853 2262.39,87.9854 \n",
       "  2263.4,87.9856 2264.4,87.9858 2265.41,87.9859 2266.41,87.9861 2267.42,87.9863 2268.42,87.9865 2269.42,87.9867 2270.43,87.9868 2271.43,87.987 2272.44,87.9872 \n",
       "  2273.44,87.9874 2274.45,87.9876 2275.45,87.9878 2276.45,87.988 2277.46,87.9883 2278.46,87.9885 2279.47,87.9887 2280.47,87.9889 2281.48,87.9892 2282.48,87.9894 \n",
       "  2283.49,87.9896 2284.49,87.9899 2285.49,87.9901 2286.5,87.9904 2287.5,87.9906 2288.51,87.9909 2289.51,87.9911 2290.52,87.9914 2291.52,87.9917 2292.52,87.992 \n",
       "  \n",
       "  \"/>\n",
       "<path clip-path=\"url(#clip280)\" d=\"\n",
       "M1992.92 198.898 L2281.82 198.898 L2281.82 95.2176 L1992.92 95.2176  Z\n",
       "  \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<polyline clip-path=\"url(#clip280)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1992.92,198.898 2281.82,198.898 2281.82,95.2176 1992.92,95.2176 1992.92,198.898 \n",
       "  \"/>\n",
       "<polyline clip-path=\"url(#clip280)\" style=\"stroke:#009af9; stroke-linecap:butt; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  2016.57,147.058 2158.45,147.058 \n",
       "  \"/>\n",
       "<path clip-path=\"url(#clip280)\" d=\"M2195.94 166.745 Q2194.13 171.375 2192.42 172.787 Q2190.7 174.199 2187.83 174.199 L2184.43 174.199 L2184.43 170.634 L2186.93 170.634 Q2188.69 170.634 2189.66 169.8 Q2190.64 168.967 2191.82 165.865 L2192.58 163.921 L2182.09 138.412 L2186.61 138.412 L2194.71 158.689 L2202.81 138.412 L2207.33 138.412 L2195.94 166.745 Z\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" /><path clip-path=\"url(#clip280)\" d=\"M2214.62 160.402 L2222.26 160.402 L2222.26 134.037 L2213.95 135.703 L2213.95 131.444 L2222.21 129.778 L2226.89 129.778 L2226.89 160.402 L2234.52 160.402 L2234.52 164.338 L2214.62 164.338 L2214.62 160.402 Z\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" /></svg>\n"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V2(x) =  V0*exp(-(x+x0)^2)\n",
    "mat_H2 = make_H1dp(N,xmax,xmin,V2) \n",
    "energy2,mat_v2 = eigen(mat_H2)\n",
    "println(energy2[1])\n",
    "ψ2 = mat_v2[:,1]\n",
    "using Plots\n",
    "plot(xvec,ψ2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "となるので、行列は"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "calc_Htb (generic function with 1 method)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function calc_Htb(energy1,ψ1,ψ2,vecV1)\n",
    "    mat_Htb = zeros(Float64,2,2)\n",
    "    \n",
    "    t = 0.0\n",
    "    v0 = 0.0\n",
    "    N = length(ψ1)\n",
    "    for i=1:N        \n",
    "        t += (energy[1]+vecV1[i])*ψ1[i]*ψ2[i]\n",
    "        v0 += vecV1[i]*ψ2[i]*ψ2[i]\n",
    "    end\n",
    "    mat_Htb[1,1] = energy[1]+v0\n",
    "    mat_Htb[1,2] = t\n",
    "    mat_Htb[2,1] = t\n",
    "    mat_Htb[2,2] = energy[1]+v0\n",
    " \n",
    "    \n",
    "    return mat_Htb\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Float64}:\n",
       " -3.1404      -0.00306652\n",
       " -0.00306652  -3.1404"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 2000\n",
    "xmax = 10.0\n",
    "xmin = -10.0\n",
    "vecV1 = zeros(Float64,N)\n",
    "dx = (xmax-xmin)/(N-1)\n",
    "for i=1:N\n",
    "    x = (i-1)*dx+xmin\n",
    "    vecV1[i] = V1(x) \n",
    "end\n",
    "mat_Htb = calc_Htb(energy1,ψ1,ψ2,vecV1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "となる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.1434681456481526, -3.1373351107965433]\n",
      "[0.7071067811865475, 0.7071067811865475]\n"
     ]
    }
   ],
   "source": [
    "ε,c = eigen(mat_Htb)\n",
    "println(ε)\n",
    "println(c[1:2,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最低固有値の固有関数は、結合性軌道であることがわかる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ポテンシャル二つの時のエネルギー\n",
      "[-3.1408706997702507, -3.139831443637112, -0.44623596291542933, -0.35515999810553556, 0.07018456954411345, 0.310156460019972, 0.42911267028300504, 0.894830194668943, 0.9798593010634473, 1.7431435321999604]\n"
     ]
    }
   ],
   "source": [
    "V0 = -5.0\n",
    "x0 = 3\n",
    "\n",
    "xvec = range(xmin,xmax,length=N)\n",
    "V12(x) =  V0*(exp(-(x-x0)^2)+exp(-(x+x0)^2))\n",
    "mat_H2 = make_H1dp(N,xmax,xmin,V12) \n",
    "energy2p,mat_v2 = eigen(mat_H2)\n",
    "println(\"ポテンシャル二つの時のエネルギー\")\n",
    "println(energy2p[1:10])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "値は少しだけずれているが、だいたい再現していると言える。このズレは、離散化や積分の誤差から来ているかもしれない。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 タイトバインディング模型\n",
    "さて、最後に作った行列は、$2\\times 2$のサイズであった。この形まで持ってくると、もはやどのような束縛状態であったのかは見た目からはわからない。\n",
    "束縛状態の形は、この行列の非対角要素や対角要素の値に反映されている。  \n",
    "つまり、原子核に電子が束縛されている時も同じような方法で束縛状態だけを取ってくることで、簡単な行列の形に持ってくることができる。\n",
    "これが「タイトバインディング模型」である。  \n",
    "固体中の物質の性質は、「束縛された電子の波動関数がとなりとどのくらいオーバーラップしているか」で決まっている。\n",
    "\n",
    "最後に、ポテンシャルが四つある場合をこの模型で再現してみよう。簡単のため、対角要素に入っていた積分は全てゼロと置き、非対角要素だけを考える。また、束縛状態は十分に局在しているため、オーバーラップは隣以外を無視する。\n",
    "この時、ハミルトニアンは、\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "calc_HtbModel (generic function with 1 method)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function calc_HtbModel(energy1,ψ1,ψ2,vecV1,Nx)\n",
    "    mat_Htb = zeros(Float64,Nx,Nx)\n",
    "    \n",
    "    t = 0.0\n",
    "    v0 = 0.0\n",
    "    N = length(ψ1)\n",
    "    for i=1:N        \n",
    "        t += (energy[1]+vecV1[i])*ψ1[i]*ψ2[i]\n",
    "    end\n",
    "    \n",
    "    for i =1:Nx\n",
    "        for dx in -1:1\n",
    "            j = i + dx\n",
    "            j += ifelse(j > Nx,-Nx,0)\n",
    "            j += ifelse(j < 1,Nx,0)\n",
    "            \n",
    "            if dx ==0\n",
    "                mat_Htb[i,j] = energy[1]\n",
    "            elseif abs(dx) == 1   \n",
    "                mat_Htb[i,j] = t    \n",
    "            end\n",
    "        end\n",
    "    end \n",
    "    \n",
    "    return mat_Htb\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Matrix{Float64}:\n",
       " -3.1404      -0.00306652   0.0         -0.00306652\n",
       " -0.00306652  -3.1404      -0.00306652   0.0\n",
       "  0.0         -0.00306652  -3.1404      -0.00306652\n",
       " -0.00306652   0.0         -0.00306652  -3.1404"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 2000\n",
    "xmax = 10.0\n",
    "xmin = -10.0\n",
    "vecV1 = zeros(Float64,N)\n",
    "dx = (xmax-xmin)/(N-1)\n",
    "for i=1:N\n",
    "    x = (i-1)*dx+xmin\n",
    "    vecV1[i] = V1(x) \n",
    "end\n",
    "mat_Htb = calc_HtbModel(energy1,ψ1,ψ2,vecV1,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.1465339388661384, -3.1404009040145286, -3.1404009040145286, -3.134267869162919]\n",
      "[-0.4999999999999999, -0.5000000000000007, -0.4999999999999999, -0.4999999999999991]\n",
      "[-3.1464447984917503, -3.1404344051833117, -3.1403806125861387, -3.1342700928874323, -0.5439642693009712, -0.3966847995080151, -0.39613473223049867, -0.14398863565515585, 0.4934084688978966, 1.0192066655092875]\n"
     ]
    }
   ],
   "source": [
    "ε4,c4 = eigen(mat_Htb)\n",
    "println(ε4)\n",
    "println(c4[:,1])\n",
    "println(energy4p[1:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "となるので、エネルギーはよく一致している。  \n",
    "### 1.4 このノートのまとめ\n",
    "以上から、電子の束縛状態同士が近い場合、その波動関数のオーバーラップによってエネルギーの縮退が解けることがわかった。\n",
    "また、このオーバーラップを非対角要素とした模型「タイトバインディング模型」を使うことで、それぞれの束縛状態の情報をホッピングの強弱に押し込めることができた。\n",
    "また、このような模型を用いることにより、取り扱える長さスケールが大幅に長くなったことも注目すべきである。つまり、もともとは微分方程式を差分化した差分化の幅など非常に小さな長さスケールを使って方程式を議論していたが、タイトバインディング模型に変えたことにより、最小の長さスケールはポテンシャルとポテンシャルの距離、つまり原子間距離にまで伸びた。これによって、原子が数百並んだような問題を考えることができるようになり、トポロジカル絶縁体など端が重要となる物理を議論することができるようになる。\n",
    "\n",
    "なお、実際の電子は水素原子のように、s軌道、d軌道、p軌道などの束縛状態を持つ。そして、s軌道とs軌道、s軌道とp軌道の重なり積分がどうなっているか、ということを用いたモデルの構築方法は、「Slater-Kosterの方法」と呼ばれている。  \n",
    "http://wyvern.phys.s.u-tokyo.ac.jp/f/lecture/corrcondmat/slater-koster.htm   \n",
    "このウェブサイトに、それぞれの値がまとめられている。  \n",
    "\n",
    "ここまでは一次元シュレーディンガー方程式から出発してタイトバインディング模型の導出までであったが、次回以降は、フェルミ統計性を利用して固体中の物性について述べようと思う。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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