Semirelativistic Bound-State Equations: Trivial Considerations

TL;DR

This paper discusses the eigenvalue problem of the spinless Salpeter equation, providing elementary tools and insights for approximate solutions in relativistic bound-state models using specific potentials.

Contribution

It offers a review of simple analytical methods for solving the spinless Salpeter equation with Woods-Saxon and Hulthén potentials, highlighting practical approaches for bound-state problems.

Findings

Elementary tools for approximate solutions are illustrated.

Applications to Woods-Saxon and Hulthén potentials are demonstrated.

Provides insights into relativistic bound-state eigenvalue problems.

Abstract

Observing renewed interest in long-standing (semi-) relativistic descriptions of bound states, we would like to make a few comments on the eigenvalue problem posed by the spinless Salpeter equation and, illustrated by the examples of the nonsingular Woods-Saxon potential and the singular Hulth\'en potential, recall elementary tools that practitioners looking for analytic albeit approximate solutions might find useful in their quest.