Analytical approximations to the l-wave solutions of the Schrödinger equation with the Eckart potential

The bound-state solutions of the Schrödinger equation with the Eckart potential with the centrifugal term are obtained approximately. It is shown that the solutions can be expressed in terms of the generalized hypergeometric functions ₂F₁(a, b; c; z). The intractable normalized wavefunctions are also derived. To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other methods for short-range potential (large a). Two special cases for l = 0 and β = 0 are also studied briefly.