Solutions of the scattering problem in a complete set of Bessel functions with a discrete index

TL;DR

This paper develops solutions to the radial Schrödinger equation for scattering states using Bessel function series, applying the method to electron scattering off molecules with multipole moments.

Contribution

It introduces a novel approach using a complete set of Bessel functions with a discrete index for solving scattering problems in quantum mechanics.

Findings

Solutions expressed as convergent Bessel series for various potentials

Application to electron scattering with multipole moments

Enhanced understanding of scattering states in complex potentials

Abstract

We use the tridiagonal representation approach to solve the radial Schr\"odinger equation for the continuum scattering states of the Kratzer potential. We do the same for a radial power-law potential with inverse-square and inverse-cube singularities. These solutions are written as infinite convergent series of Bessel functions with a discrete index. As physical application of the latter solution, we treat electron scattering off a neutral molecule with electric dipole and electric quadrupole moments.