The nature of the electronic states of a disordered system. I. Localized states

Abstract

An electron in a random array of dense, weak scatterers is presented as a model which is expected to exhibit the typical features of a disordered system. An average Green function for the electron is defined and derived as a Feynman path integral. In this formulation there is a clear similarity of the problem to that of a nonmarkovian random chain and this is used to further the understanding of the problem. A selfconsistent method of solving the path integral for the average Green function is proposed and then used to elucidate the nature of the localized electronic states of the system. Particular attention is paid to states at the mobility edge and the spatial extent of the wavefunction near the edge is shown to behave as mod E-E_c mod ^-35/.