Approximate l-States of the Manning-Rosen Potential by Using Nikiforov-Uvarov Method. (4th April 2012) - Ikhdair, Sameer M.
Abstract : 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 principal and orbital quantum numbers n and l with two different values of the potential screening parameter α . It is found that our results are in good agreement with the those obtained by other methods for short potential range, lowest values of orbital quantum number l, and α . Two special cases of much interest are investigated like the s -wave case and Hulthén potential case.