A semirelativistic treatment of spinless particles subject to the Yukawa potential with arbitrary angular momenta

TL;DR

This paper derives analytical semi-relativistic solutions for spinless particles under the Yukawa potential, comparing approximate and exact numerical spectra, and explores special cases like the Coulomb potential.

Contribution

It provides a new semi-relativistic analytical approach to the Yukawa potential using the Nikiforov-Uvarov method, including comparison with exact numerical results.

Findings

Approximate analytical energy spectra agree well with exact numerical results for lower states.

Derived normalized wave functions for the bound states.

Analyzed special cases such as the nonrelativistic limit and Coulomb potential.

Abstract

We obtain analytical solutions of the two-body spinless Salpeter (SS) equation with Yukawa potential within the conventional approximation scheme to the centrifugal term for any -state. The semi-relativistic bound state energy spectra and the corresponding normalized wave functions are calculated by means of the Nikiforov-Uvarov (NU) method. We also obtain the numerical energy spectrum of the SS equation without any approximation to centrifugal term for the same potential and compare them with the approximated numerical ones obtained from the analytical expressions. It is found that the exact numerical results are in good agreement with the approximated ones for the lower energy states. Special cases are treated like the nonrelativistic limit and the solution for the Coulomb problem.