Analytical Solution of two-body spinless Salpeter Equation for Hellmann Potential

TL;DR

This paper derives analytical solutions for the two-body spinless Salpeter equation with the Hellmann potential, providing explicit energy levels and eigenfunctions, and explores special cases like Yukawa and Coulomb potentials.

Contribution

It presents the first analytical expressions for energy levels and eigenfunctions of the spinless Salpeter equation with the Hellmann potential using functional analysis.

Findings

Analytical energy levels derived for the Hellmann potential.

Eigenfunctions expressed in terms of hypergeometric functions.

Special cases for Yukawa and Coulomb potentials analyzed.

Abstract

Approximate bound state solutions of the spinless Salpeter equation for the Hellmann potential are studied for heavy particles. By using functional analysis method, an analytical expression for the energy levels, and the corresponding eigenfunctions of the system are obtained in terms of the hypergeometric functions. The analytical results for the Yukawa and Coulomb potentials are also studied as special cases.