Any l-state approximate solutions of the Manning-Rosen potential by the Nikiforov-Uvarov method

TL;DR

This paper uses the Nikiforov-Uvarov method to find approximate bound state energies and wave functions for the Manning-Rosen potential in the Schrödinger equation, demonstrating good agreement with other methods.

Contribution

It provides a new approximate analytical solution for the Manning-Rosen potential using the NU method, including cases with arbitrary quantum numbers and potential parameters.

Findings

Eigenvalues agree with other methods for short potential range and small l.

Wave functions are expressed via Jacobi polynomials.

Solution reduces to known cases like l=0 and Hulthen potential.

Abstract

The Schrodinger equation for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states energies. Additionally, the corresponding wave functions are expressed by the Jacobi polynomials. The Nikiforov-Uvarov (NU) method is used in the calculations. To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l with two different values of the potential parameter \alpha. It is shown that the results are in good agreement with the those obtained by other methods for short potential range, small l and \alpha. This solution reduces to two cases l=0 and Hulthen potential case.