Bound State Solutions of the Schr\"odinger Equation for Generalized Morse Potential With Position Dependent Mass

TL;DR

This paper analytically solves the one-dimensional Schrödinger equation with a generalized Morse potential and position-dependent mass, providing energy eigenvalues and eigenfunctions, with numerical results for diatomic molecules that agree with previous studies.

Contribution

It introduces an analytical solution method for the Schrödinger equation with a generalized Morse potential and position-dependent mass, extending prior work to more complex mass distributions.

Findings

Analytical expressions for energy eigenvalues and eigenfunctions.

Numerical results for specific diatomic molecules.

Results consistent with previous studies.

Abstract

The effective mass one-dimensional Schr\"odinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the case of constant mass. Energy eigenvalues are computed numerically for some diatomic molecules. The results are in agreement with the ones obtained before.