Energy states of some diatomic molecules: Exact quantization rule approach

TL;DR

This paper derives approximate analytical solutions for the radial Schrödinger equation of Deng-Fan diatomic molecules using the exact quantization rule, providing energy levels that align well with previous results and extending to rotational-vibrational states.

Contribution

It introduces an analytical method using the exact quantization rule to solve for energy states of diatomic molecules with the Deng-Fan potential, including rotational-vibrational extensions.

Findings

Energy levels agree with previous shifted Deng-Fan results

Wave functions expressed via hypergeometric functions

Extended to rotational-vibrational energy eigenvalues

Abstract

In this study, we obtain the approximate analytical solutions of the radial Schr\"{o}dinger equation for the Deng-Fan diatomic molecular potential by using exact quantization rule approach. The wave functions have been expressed by hypergeometric functions via the functional analysis approach. An extension to rotational-vibrational energy eigenvalues of some diatomic molecules are also presented. It is shown that the calculated energy levels are in good agreement with the ones obtained previously $E_{n\ell}-D$ (shifted Deng-Fan).