Relativistic Treatment of the Hellmann-generalized Morse potential

TL;DR

This paper presents a relativistic approach to solving the Hellmann-generalized Morse potential using the Klein-Gordon and Dirac equations, deriving eigenfunctions and energy levels for diatomic molecules, and confirming consistency with existing literature.

Contribution

It introduces a relativistic solution method for the Hellmann-generalized Morse potential, including eigenfunctions, and applies it to diatomic molecules, extending previous non-relativistic models.

Findings

Eigenvalues agree with literature values

Eigenfunctions derived explicitly

Relativistic effects analyzed for diatomic molecules

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, and wavefunctions reduced to the non-relativisitc energy Equation. The bound state energy eigenvalues for N_2, 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.