Approximate l-state solutions of the D-dimensional Schrodinger equation for Manning-Rosen potential

TL;DR

This paper presents an approximate analytical solution to the D-dimensional Schrödinger equation with Manning-Rosen potential using the NU method, including numerical results and interdimensional degeneracy analysis.

Contribution

It introduces an approximate method for solving the D-dimensional Schrödinger equation with Manning-Rosen potential and explores interdimensional degeneracy of eigenvalues.

Findings

Numerical energy eigenvalues for 2D and 4D systems are provided.

Eigenvalues exhibit interdimensional degeneracy, allowing transformation between dimensions.

Solution reduces to the Hulthén potential case.

Abstract

The Schr\"{o}dinger equation in $D$-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions). The Nikiforov-Uvarov(NU) method is used in the calculations. We present numerical calculations of energy eigenvalues to two- and four-dimensional systems for arbitrary quantum numbers $n$ and $l$ with three different values of the potential parameter $\alpha .$ It is shown that because of the interdimensional degeneracy of eigenvalues, we can also reproduce eigenvalues of a upper/lower dimensional sytem from the well-known eigenvalues of a lower/upper dimensional system by means of the transformation $(n,l,D)\to (n,l\pm 1,D\mp 2)$. This solution reduces to the Hulth\'{e}n potential case.