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: