An expansion of continuum wave functions in terms of resonant states: (II). Solvable models

Abstract

This paper applies the formalism developed in part I which provides a purely discrete expansion for a continuum wave solution of the Schrödinger equation in terms of resonant states along the interior region of a finite range interaction. We consider two exactly solvable models for several values of the distance and momenta on and off resonance. Our results are compared with a recent approach by Bang and collaborators which involves subtraction terms. It is found that along the internal region the subtraction terms are not in general negligible. Our work substantiates an expression for the continuum wave function near resonance. We also obtain an equation for time delay in terms of resonant states.