Moment Singularity Expansion for the Density of States

Abstract

A systematic approximation procedure is developed to determine the density of states associated with a particular energy band. The density of states is expressed as the sum of two functions, one of which contains the discontinuous derivatives produced by critical points, and is determined once the effective masses at these points are known; the other is smooth, and is expanded in Jacobi polynomials. The coefficients in this expansion are determined from the moments of the distribution. Two applications of the method are given.