An improved approximation to l-wave bound states of the Manning-Rosen potential by Nikiforov-Uvarov method

TL;DR

This paper introduces a new approximation method for solving the Schrödinger equation with Manning-Rosen potential for l-wave states, providing accurate energy eigenvalues and wave functions, and validating results with numerical calculations for diatomic molecules.

Contribution

A novel approximation scheme for the centrifugal term in the Manning-Rosen potential problem, enabling analytical solutions for l-wave states with improved accuracy.

Findings

Numerical energy eigenvalues agree well with numerical integration results.

Wave functions expressed in terms of Jacobi polynomials.

Method reduces to known cases like s-wave and Hulthén potential.

Abstract

A new approximation scheme to the centrifugal term is proposed to obtain the $l\neq 0$ solutions of the Schr\"{o}dinger equation with the Manning-Rosen potential. We also find the corresponding normalized wave functions in terms of the Jacobi polynomials. To show the accuracy of the new approximation scheme, we calculate the energy eigenvalues numerically for arbitrary quantum numbers $n$ and $l$ with two different values of the potential parameter $\alpha .$ The bound state energies of various states for a few $% HCl,$ $CH,$ $LiH$ and $CO$ diatomic molecules are also calculated. The numerical results are in good agreement with those obtained by using program based on a numerical integration procedure. Our solution can be also reduced to the s-wave ($l=0$) case and to the Hulth\'{e}n potential case.