All l-state eigensolutions of the non-relativistic Schrodinger equation with the general molecular oscillator

TL;DR

This paper derives analytical approximate solutions for the Schrödinger equation with a general molecular oscillator, providing explicit energy eigenvalues and wave-functions, and applies the method to diatomic molecules with results aligning well with existing literature.

Contribution

It introduces an exact quantization rule approach with improved Pekeris-type approximations for solving the Schrödinger equation with a general molecular oscillator, including special cases like Morse and Deng-Fan potentials.

Findings

Derived explicit energy eigenvalues and wave-functions for the GMO.

Applied the method to diatomic molecules such as H2, CO, HCl, and LiH.

Results agree well with existing literature.

Abstract

In this study, we employ exact quantization rule (EQR) to derive the analytical approximate l-wave solutions of the Schrodinger equation with the general molecular oscillator (GMO). The energy eigenvalues equation and the corresponding wave -functions have been obtained explicitly. Improved Pekeris-type approximation Schemes have been used to deal with the orbital centrifugal term. We have deduced expressions for the bound-state energy eigenvalues of the Morse and shifted Deng-Fan oscillator as special cases of the GMO, and computed their resulting bound-state energy eigenvalues for H2, CO, HCl and LiH diatomic molecules. Our results are in good agreement with other results in the literature.