The Scattering amplitude for Rationally extended shape invariant Eckart potentials

Abstract: We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally ex- tended potentials is calculated analytically for the generalized mth (m = 1, 2, 3, ...) case by considering the asymptotic behavior of the scattering state wave functions which are written in terms of some new polynomials related to the Jacobi polyno- mials. As expected, in the m = 0 limit, this scattering amplitude goes over to the scattering amplitude for the conventional Eckart potential.