# The Spinless Relativistic Hellmann Problem

## TL;DR

This paper analyzes the discrete eigenvalue spectra of spinless Salpeter equations with combined Coulomb and Yukawa potentials, offering insights to guide relativistic bound state modeling.

## Contribution

It provides a compilation of easily deducible spectral information for a class of relativistic equations with generalized Hellmann potentials, aiding future bound state studies.

## Key findings

- Spectral properties of the relativistic Hamiltonian are characterized.
- Guidelines for modeling relativistic bound states are proposed.
- Generalizations of the Hellmann potential are analyzed.

## Abstract

We compile some easily deducible information on the discrete eigenvalue spectra of spinless Salpeter equations encompassing, besides a relativistic kinetic term, interactions which are expressible as superpositions of an attractive Coulomb potential and an either attractive or repulsive Yukawa potential and, hence, generalizations of the Hellmann potential employed in several areas of science. These insights should provide useful guidelines to all attempts of finding appropriate descriptions of bound states by (semi-) relativistic equations of motion.