Non-Relativistic Phase Shifts via Laplace Transform Approach

TL;DR

This paper introduces a Laplace transform method to analytically compute scattering phase shifts and wave functions for a Mie-type potential, also deriving bound state spectra.

Contribution

It presents a novel application of Laplace transform techniques to derive phase shifts and bound states for specific potentials, enhancing analytical solutions in quantum scattering.

Findings

Analytical expressions for phase shifts obtained

Bound state spectra derived explicitly

Normalized wave functions characterized

Abstract

The Laplace transform approach with convolution theorem is used to find the scattering phase shifts of a Mie-type potential. The normalized scattering wave functions are also studied. The bound state spectrum and the corresponding normalized wave functions are obtained with the help of the analytical properties of the scattering amplitude.