On the bound-state solutions of the Manning–Rosen potential including an improved approximation to the orbital centrifugal term

Abstract

The approximate analytical bound-state solution of the Schrödinger equation for the Manning–Rosen (MR) potential is found by taking a new approximation scheme to the orbital centrifugal term. The Nikiforov–Uvarov method is used in the calculations. We obtain analytic forms for the energy eigenvalues and the corresponding normalized wave functions in terms of Jacobi polynomials or hypergeometric functions for different screening parameters 1/b. The rotational–vibrational energy states for a few diatomic molecules are calculated for arbitrary quantum numbers n and l with different values of the potential parameter α. The present numerical results agree within five decimal digits with the previously reported results for different 1/b values. A few special cases of the s-wave (l=0) MR potential and the Hulthén potential are also studied.