On the generalized Morse potential

Abstract

The equivalence between the generalized Morse (GMP) and Eckart potentials is shown. The study of the hypergeometric Natanzon potentials using SO(2,1) techniques is applied to compute the eigenfunctions and eigenvalues of the Eckart (GMP) potential. The action of the group generators is studied, with the result that a family of Eckart potentials is obtained which is different from the one obtained in SUSYQM.