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

TL;DR

This paper derives analytical solutions for the Schrödinger equation with the Manning-Rosen potential using a new approximation for the centrifugal term, providing accurate energy levels and wave functions for diatomic molecules.

Contribution

It introduces a novel approximation scheme for the centrifugal term and applies the Nikiforov-Uvarov method to obtain explicit bound state solutions.

Findings

Analytic energy eigenvalues and wave functions are derived.

Results agree with previous studies within five decimal digits.

Special cases like s-wave Manning-Rosen and Hulthén potentials are analyzed.

Abstract

The approximate analytical bound state solution of the Schr\"odinger equation for the Manning-Rosen potential is carried out 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 the 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 {\alpha}. 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) Manning-Rosen potential and the Hulth\'en potential are also studied. Keywords: Energy eigenvalues; Manning-Rosen potential; Nikiforov-Uvarov method, Approximation schemes. 03.65.-w; 02.30.Gp; 03.65.Ge; 34.20.Cf