Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials

TL;DR

This paper develops approximate analytical solutions for the rotational-vibrational energy spectra of diatomic molecules using hyperbolical potentials, employing the Nikiforov-Uvarov method to derive closed-form expressions.

Contribution

It introduces a new approximate analytical approach to solve the Schrödinger equation for diatomic molecules with hyperbolical potentials, providing explicit energy spectra and wavefunctions.

Findings

Derived closed-form energy spectra and wavefunctions in terms of hypergeometric functions.

Calculated numerical energy levels for H2 and Ar2 molecules.

Compared results with previous models and experimental data, showing good agreement.

Abstract

The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate ro-vibratinal energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials P_{n}^{(\mu,\nu)}(x), where \mu>-1, \nu>-1 and x included in [-1,+1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H_{2} and Ar_{2} molecules are also calculated and compared with the previous models and experiments.