Analytical approximations to the solutions of the Manning-Rosen potential with centrifugal term

摘要

The bound state solutions of the Manning-Rosen potential with the centrifugal term are presented approximately. It is shown that the solutions can be expressed by the generalized hypergeometric functions F-2(1)(a, b; c; z). The intractable normalized wavefunctions are derived. 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 parameter alpha. It is found that the results are in good agreement with those obtained by other method for short potential range, small 1 and alpha. Two special cases for l = 0 and the Hulthen potential are also studied briefly. (c) 2007 Elsevier B.V. All rights reserved.