Density of Electronic Energy Levels for a One-Dimensional Liquid

Abstract

Preliminary to a three‐dimensional calculation, the density of one‐electron energy levels for a one‐dimensional array of square wells whose positions are Gaussianly distributed independent random variables has been calculated. The Hamiltonian matrix elements are calculated using the tight‐binding approximation and the Montroll moment‐trace method is used to compute the first six moments of the density of states curve. Hermite and Legendre polynomial expansions are then used to obtain the density of states curve itself. This method is, of course, valid independent of dimension. The integrated density of states curve as here obtained agrees nicely with the computer solution given by Landauer and Helland.