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

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 F12(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 α. It is found that the results are in good agreement with those obtained by other method for short potential range, small l and α  . Two special cases for l=0l=0 and the Hulthén potential are also studied briefly.