Approximated l-states of the Manning-Rosen potential by Nikiforov-Uvarov method

TL;DR

This paper derives approximate analytical solutions for the bound states of the Manning-Rosen potential using the Nikiforov-Uvarov method, providing energy spectra and wave functions with numerical validation.

Contribution

It introduces a new approximation approach for the centrifugal term and applies the NU method to obtain analytical solutions for the Manning-Rosen potential.

Findings

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

Energy eigenvalues are accurately calculated for various quantum numbers.

Special cases like s-wave and Hulthén potential are also analyzed.

Abstract

The approximately analytical bound state solutions of the l-wave Schr\"odinger equation for the Manning-Rosen (MR) potential are carried out by a proper approximation to the centrifugal term. The energy spectrum formula and normalized wave functions expressed in terms of the Jacobi polynomials are both obtained for the application of the Nikiforov-Uvarov (NU) method to the Manning-Rosen potential. 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 found that our results are in good agreement with the those obtained by other methods for short potential range, small l and {\alpha}. Two special cases are investigated like the s-wave case and Hulth\'en potential case.