An expansion of continuum wave functions in terms of resonant states

Abstract

The poles and residues of the complete outgoing Green function in the complex momentum plane are used to obtain, in the case of finite range potentials, an eigenfunction expansion of the continuum wave solution. It is found that in the region r< a the wave solution may be expressed as an infinite sum of discrete terms involving the bound, antibound and resonant states of the problem. At the boundary radius r = a a different expansion is obtained. In this case, in order to get an infinite discrete sum, one has to introduce two subtraction terms. Otherwise the expansion is given by a finite sum of discrete terms and an