The Scattering amplitude for Newly found exactly solvable Potential

TL;DR

This paper explicitly calculates the scattering amplitude for a new exactly solvable shape invariant potential, expanding understanding of quantum scattering in systems related to exceptional Jacobi polynomials.

Contribution

It provides the first explicit calculation of the scattering amplitude for a recently discovered shape invariant potential linked to exceptional Jacobi polynomials.

Findings

Scattering amplitude derived explicitly for the new potential

Potential is isospectral to the generalized Pöschl-Taylor potential

Connects exceptional polynomials with quantum scattering analysis

Abstract

The scattering amplitude for the recently discovered exactly solvable shape invariant potential, which is isospectral to the generalized P\"oschl-Taylor potential, is calculated explicitly by considering the asymptotic behavior of the $X_{1}$ Jacobi exceptional polynomials associated with this system.