Analytical solutions of the Schr\"{o}dinger equation with the Manning-Rosen potential plus a Ring-Shaped like potential

TL;DR

This paper derives analytical solutions for the Schrödinger equation with a combined Manning-Rosen and ring-shaped potential, providing explicit energy levels and eigenfunctions for arbitrary angular momentum states.

Contribution

It introduces an analytical approach using the Nikiforov-Uvarov method with an improved approximation for the centrifugal term, extending solutions to arbitrary l-states.

Findings

Explicit energy spectra for the combined potential.

Normalized eigenfunctions expressed in orthogonal polynomials.

Method applicable to arbitrary angular momentum states.

Abstract

The analytical solution of the Schr\"{o}dinger equation for the Manning-Rosen potential plus a ring-shaped like potential is obtained by applying the Nikiforov-Uvarov method by using the improved approximation scheme to the centrifugal potential for arbitrary $l$ states. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary $l$ states.