Relativistic treatment of the hellmann-generalized morse potential

Abstract

We solve the relativistic equations (Klein-Gordon and Dirac equation) via the conventional Nikiforov-Uvarov method. In order to overcome the centrifugal barrier, we employed the well-known Greene and Aldrich approximation scheme. The corresponding normalized eigenfunctions was also obtained in each case. It was shown that in the non-relativistic limits, both energy equations obtained by solving Klein-Gordon and Dirac equations, as well as the wavefunctions reduced to the non-relativisitc energy equation. The bound state energy eigenvalues for N2, CO, NO, CH and HCl diatomic molecules were computed for various vibrational and rotational quantum numbers. It was found that our results agree with those in literature.