The electronic structure of disordered systems

Abstract The problem of the states of electrons moving under the influence of disordered scattering centres is discussed in the simplest case of one dimension and weak interaction. It is shown how to define a density of levels n(E) and an energy and momentum density p(k, E) and the variation of those functions from the case of completely disordered scattering centres to the completely ordered case is discussed. In the weak interaction case it is long-range order which dominates the problem and the effect of even slight disorder results in the appearance of states inside the energy gap of the ordered system.