The Scattering amplitude for one parameter family of shape invariant potentials related to Xm Jacobi polynomials

TL;DR

This paper calculates the scattering amplitude for a new family of exactly solvable shape invariant potentials related to Xm Jacobi polynomials, extending understanding of their quantum scattering properties.

Contribution

It provides an explicit calculation of the scattering amplitude for a recently discovered one parameter family of shape invariant potentials linked to Xm Jacobi polynomials.

Findings

Explicit scattering amplitude expressions derived

Potential family is isospectral to generalized Pöschl-Teller

Asymptotic analysis of Xm Jacobi polynomials conducted

Abstract

We consider the recently discovered, one parameter family of exactly solvable shape invariant potentials which are isospectral to the generalized P\"oschl-Teller potential. By explicitly considering the asymptotic behaviour of the Xm Jacobi polynomials associated with this system (m = 1, 2, 3, ...), the scattering amplitude for the one parameter family of potentials is calculated explicitly.