Analytic Properties of Radial Wave Functions

Abstract

This is a review article about the properties of radial wave functions and other quantities relevant to the partial wave analysis of scattering theory, as functions of the energy or wave number. The treatment is restricted to the nonrelativistic Schrödinger equation for two particles with a local potential. In addition to regular and irregular solutions of the radial differential equations, the Jost function, S matrix, and Green's functions are analyzed and completeness is proved. The examples investigated in detail include the Bargmann potentials and their generalizations.