Bound state solutions of the Manning-Rosen potential

TL;DR

This paper uses the asymptotic iteration method to derive analytical solutions for the Schrödinger equation with the Manning-Rosen potential, providing accurate eigenvalues for diatomic molecules and extending to special cases.

Contribution

It introduces a novel application of AIM with three Pekeris-type approximations for solving the Manning-Rosen potential in quantum mechanics.

Findings

Eigenvalues agree well with existing literature

Accurate solutions for diatomic molecules like HCl and CO

Extension to s-wave and Hulthén potentials

Abstract

Using the asymptotic iteration method (AIM), we have obtained analytical approximations to the $\ell$-wave solutions of the Schr\"{o}dinger equation with the Manning-Rosen potential. The equation of energy eigenvalues equation and the corresponding wavefunctions have been obtained explicitly. Three different Pekeris-type approximation schemes have been used to deal with the centrifugal term. To show the accuracy of our results, we have calculated the eigenvalues numerically for arbitrary quantum numbers $n$ and $\ell$ for some diatomic molecules (HCl, CH, LiH and CO). It is found that the results are in good agreement with other results found in the literature. A straightforward extension to the s-wave case and Hulth$\acute{e}$n potential case are also presented.