'grid fix'

ch03/fourier_transform.ipynb

@@ -28,7 +28,7 @@
     "\n",
     ":::\n",
     "\n",
-    "### Fourier coeffiecients\n",
+    ":::{admonition} **Fourier coeffiecients and orthogonality of sin and cos functions**\n",
     "\n",
     "- Using the orthogonality property of the cos and sin functions we can determine an expression for the coefficients of the Fourier Series. By integrating the Fourier Series over the interval [-${\\pi}$,${\\pi}$], we can determine an expression for $a_0$. Over this interval, the sums will vanish, as we are intergrating the $\\sin$ and $\\cos$ functions over one period. Thus, we are left with\n",
     "\n",
@@ -50,7 +50,9 @@
     "\n",
     "- To determine the values of the $b_n$ coefficients we multiply by $\\sin(mx)$. Similarly to the $a_n$ coefficients, due to the orthogonality property, the only term that does not vanish on the right-hand side is $\\int_{-{\\pi}}^{\\pi}b_n\\sin(nx)\\sin(mx)dx$ for $m=n$. Thus, solving for $b_n$\n",
     "\n",
-    "$$b_n = \\frac{1}{\\pi} \\int_{-{\\pi}}^{\\pi} f(x)\\sin(nx)dx \\,\\,\\,\\,n=1, 2, ...$$\n"
+    "$$b_n = \\frac{1}{\\pi} \\int_{-{\\pi}}^{\\pi} f(x)\\sin(nx)dx \\,\\,\\,\\,n=1, 2, ...$$\n",
+    "\n",
+    ":::"
    ]
   },
   {

ch03/note05.md

@@ -150,13 +150,10 @@ $$\psi(x) = \sum_n c_n \Big(\frac{2}{L}\Big )^{1/2} sin \Big (\frac{n\pi x}{L} \
 $$c_k = \Big(\frac{2}{L}\Big )^{1/2} \int sin \Big (\frac{k\pi x}{L} \Big )\psi(x) dx$$
 :::
 
-
-
-
-
+::::
 
 
-### Probabilistic meaning of linear superposition. 
+### Probabilistic meaning of linear superposition
 
 :::{admonition} **Coefficients describe probability of observing distinct states**