Asymptotic phase shifts and Levinson theorem for 2D potentials with inverse square singularities

Abstract

The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states in a given m-th partial wave is related to the phase shift and the singularity strength of the potential. For the m-wave phase shift the asymptotic behaviour is calculated for short wavelengths.

16 pages (REVTeX)

References in corpus (2)

• Internal Modes and Magnon Scattering on Topological Solitons in 2d Easy-Axis Ferromagnets
• Phase equivalent chains of Darboux transformations in scattering theory