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

Abstract

We consider the recently discovered, one parameter family of exactly solvable shape invariant potentials which are isospectral to the generalized Pöschl–Teller potential. By explicitly considering the asymptotic behavior of the Jacobi polynomials associated with this system (), the scattering amplitude for the one parameter family of potentials is calculated explicitly.