The Scattering amplitude for one parameter family of shape invariant potentials related to Xm Jacobi polynomials (1303.3669v1)

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.