Approximate Analytical Solutions of a Two-Term Diatomic Molecular Potential with Centrifugal Barrier

TL;DR

This paper derives approximate analytical solutions for the radial Schrödinger equation with a two-term diatomic molecular potential, including special cases like Manning-Rosen, Hulthén, and Morse potentials, confirming previous results.

Contribution

It provides a unified analytical approach to solve the Schrödinger equation for various diatomic potentials with centrifugal barriers, extending existing solutions.

Findings

Analytical energy eigenvalues derived for specific potentials.

Wave functions expressed in terms of hypergeometric functions.

Results consistent with previous studies.

Abstract

Approximate analytical bound state solutions of the radial Schr\"odinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where $q\geq1$ and $q=0$. The energy eigenvalues and the corresponding normalized wave functions of the Manning-Rosen potential, the 'standard' Hulth\'{e}n potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before.