Approximate Solutions of the Fractional Schrodinger Equation for the Screened Kratzer Potential

TL;DR

This paper introduces a novel analytical approach using conformable fractional NU method to solve the fractional Schrödinger equation with the screened Kratzer potential, providing new insights into molecular energy spectra.

Contribution

The study develops a new analytical framework for solving the fractional Schrödinger equation with SKP, including numerical results for specific diatomic molecules.

Findings

Derived analytical expressions for energy spectra and eigenfunctions.

Numerical results for LiH and HCl molecules at various fractional parameters.

Graphical analysis of energy eigenvalues with respect to potential parameters.

Abstract

By employing the concept of conformable fractional Nikiforv-Uvarov (NU) method, we solved the fractional Schrodinger equation with the screened Kratzer potential (SKP). By applying the Greene-Aldrich approximation and a coordinate transformation schemes, the analytical expressions of the bound state energy spectra and eigenfunctions for SKP were obtained. Numerical results for the energies of SKP for lithium hydride and hydrogen chloride diatomic molecules were computed for different fractional parameters. Also, the graphical variation of the bound state energy eigenvalues of SKP for LiH with different potential parameters and quantum numbers were discussed, as regards the selected fractional parameters. Our results are new and have not been reported in any literature before.