Ro-vibrational energy analysis of Manning-Rosen and P\"oschl-Teller potentials with a new improved approximation in the centrifugal term

TL;DR

This paper develops an improved approximation method for calculating ro-vibrational energies in diatomic molecules using Manning-Rosen and P"oschl-Teller potentials, combining existing approximations within the Nikiforov-Uvarov framework.

Contribution

It introduces a new approximation scheme that unifies Greene-Aldrich and Pekeris-type methods for better analytical solutions of these potentials.

Findings

Derived analytical expressions for eigenvalues and eigenfunctions.

Examined energy dependence on approximation parameters $\lambda$ and $ u$.

Original approximations are recovered at specific parameter values.

Abstract

Two physically important potentials (Manning-Rosen and P\"oschl-Teller) are considered for the ro-vibrational energy in diatomic molecules. An improved new approximation is invoked for the centrifugal term, which is then used for their solution within the Nikiforov-Uvarov framework. This employs a recently proposed scheme, which combines the two widely used Greene-Aldrich and Pekeris-type approximations. Thus, approximate analytical expressions are derived for eigenvalues and eigenfunctions. The energies are examined with respect to two approximation parameters, $\lambda$ and $\nu$. The original approximations are recovered for certain specials values of these two parameters. This offers a simple effective scheme for these and other relevant potentials in quantum mechanics.