Solution of the Schrödinger equation containing a Perey-Buck nonlocality

Abstract

The solution of a radial Schrödinger equation for ψ(r) containing a nonlocal potential of the form \int{K(r,r') ψ(r') dr'} is obtained to high accuracy by means of two methods. An application to the Perey-Buck nonlocality is presented, without using a local equivalent representation. The first method consists in expanding ψ in a set of Chebyshev polynomials, and solving the matrix equation for the expansion coefficients numerically. An accuracy of between 1:10^{6} to 1:10^{14} is obtained, depending on the number of polynomials employed. The second method consists in expanding ψ into a set of N Sturmian functions of positive energy, supplemented by an iteration procedure. For N=15 an accuracy of 1:10^{4} is obtained without iterations. After one iteration the accuracy is increased to 1:10^{6}. The method is applicable to a general nonlocality K.