swave bound and scattering state wave functions for a velocitydependent Kisslinger potential
Abstract
A relation linking the normalized swave scattering and the corresponding bound state wave functions at bound state poles is derived. This is done in the case of a nonlocal, velocitydependent Kisslinger potential. Using formal scattering theory, we present two analytical proofs of the validity of the theorem. The first tackles the nonlocal potential directly, while the other transforms the potential to an equivalent local but energydependent one. The theorem is tested both analytically and numerically by solving the Schrödinger equation exactly for the scattering and bound state wave functions when the Kisslinger potential has the form of a square well. A first order approximation to the deviation from the theorem away from bound state poles is obtained analytically. Furthermore, a proof of the analyticity of the Jost solutions in the presence of a nonlocal potential term is also given.
 Publication:

European Physical Journal A
 Pub Date:
 2001
 DOI:
 10.1007/s100500170083
 Bibcode:
 2001EPJA...11..175A