Exact solutions of the s-wave Schrödinger equation with Manning-Rosen potential

The bound state solutions of the s-wave radial Schrödinger equation with Manning-Rosen potential are presented exactly by the standard method. It is found that the solutions can be expressed by the generalized hypergeometric functions ₂F₁(a, b; c; z). The intractable normalized wavefunctions are derived. We also study the special case for α≤0 and find that this potential will reduce to the Hulthén potential.