Analogies between light and electrons: Density of states and Friedel’s identity

By explicitly making use of analogies between Schr\"odinger potential scattering and classical wave scattering, we generalize statements for electron-impurity scattering to similar statements for scattering of scalar classical waves from dielectric particles. We will focus upon density of states, spectral function, Friedel's identity for screening, Wigner phase-delay time, and Thouless's criterion for localization.