Analytical approximations to the l-wave solutions of the Schrödinger equation with an exponential-type potential

The bound-state solutions of the Schrödinger equation for an exponential-type potential with the centrifugal term are presented approximately. It is shown that the complicated normalization wavefunctions can be expressed by the generalized hypergeometric functions ₂F ₁ (a, b; c; z). To show the accuracy of our results, we calculate the energy 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 another method for short-range potential. Two special cases for s-wave case (l = 0) and α = 1 are also studied briefly.