Approximate analytical solution of the Yukawa potential with arbitrary angular momenta

TL;DR

This paper derives approximate analytical solutions for the Yukawa potential in quantum mechanics, providing explicit energy levels and wavefunctions for arbitrary angular momenta, and confirms their accuracy through numerical comparisons.

Contribution

It introduces a generalized parametric NU method to solve the Yukawa potential analytically for any angular momentum, extending previous approaches.

Findings

Energy eigenvalues and eigenfunctions in closed form

Results agree with previous numerical methods

Energy levels reduce to Coulomb potential when screening parameter approaches zero

Abstract

The Yukawa potential is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schr\"odinger equation (SE) for the Yukawa potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and showed that these results are in good agreement with those are obtained previously by other methods. Also, we found the energy levels of the familiar pure Coulomb potential energy levels when the screening parameter of the Yukawa potential goes to zero.