Density_of_states

The density of states (per unit volume) is related to the spectral function. Indeed, it is (d is the dimension):

This is nothing but the trace of delta(H-E), which can be also written in configuration space (L^d is the volume of the system, not necessarily a cube...):

If we assume that the disorder is statistically invariant by tranlation, the average is the same at any position r so that it reduces to:

The density of states is thus nothing but the spectral function for an initial state being a delta-function at any point in space. This is the method used by the script compute_spectral_function.py when the initial state type point is chosen.

A better method is to additionally average over the position \bf{r}. This can be done by using an initial state with random spatially uncorrelated values of the wavefunction on all sites. This is what is done when the initial state type random is chosen. This is the recommended setting for computing the density of states.