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

The approximately analytical bound state solutions of the l-wave Schrödinger 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 α. It is found that our results are in good agreement with the those obtained by other methods for short potential range, small l and α. Two special cases are investigated like the s-wave case and Hulthén potential case.