The Generalized Fractional NU Method for the Diatomic Molecules in the Deng-Fan Model

TL;DR

This paper develops a generalized fractional NU method to solve the Deng-Fan potential in the Schrödinger equation, analyzing energy levels of diatomic molecules across various dimensions and parameters with improved accuracy.

Contribution

It introduces a novel fractional NU method for solving the Deng-Fan potential, providing analytical energy formulas and exploring effects of fractional parameters and dimensions.

Findings

Energy eigenvalues increase with fractional parameter.

Energy spectra rise with higher dimensions.

Results agree with classical cases and previous studies.

Abstract

A solution of the fractional N-dimensional radial Schrodinger equation with the Deng-Fan potential is investigated by the generalized fractional NU method. The analytical formulas of energy eigenvalues and corresponding eigen functions for the Deng-Fan potential are generated. Furthermore, the current results are applied to several diatomic molecules for the Deng-Fan potential as well as the shifted Deng Fan potential. For both the Deng-Fan potential and its shifted potential, the effect of the fractional parameter on the energy levels of various diatomic molecules is examined numerically and graphically. We found that the energy eigenvalues are gradually improved when the fractional parameter increases. The energy spectra of various diatomic molecules are also evaluated in three-dimensional space and higher dimensions. It is worthy to note that the energy spectrum raises as the number of dimensions increases. In addition, the dependence of the energy spectra of the Deng-Fan potential and its shifted potential on the reduced mass, screening parameter, equilibrium bond length, rotational and vibrational quantum numbers is illustrated. To validate our findings, we estimate the energy levels of the Deng-Fan potential and shifted Deng-Fan potential at the classical case for various diatomic molecules and found that they are entirely compatible with earlier studies.