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

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.