The Spinless Relativistic Hulth\'en Problem

TL;DR

This paper explores the spinless relativistic Hulthén problem by analyzing the eigenvalue equation involving nonlocal operators, using various techniques to rigorously constrain the bound-state spectra.

Contribution

It demonstrates the application of analytical tools to the spinless Salpeter equation with the Hulthén potential, providing insights into its bound-state spectra.

Findings

Rigorous bounds on the bound-state spectra

Application of analytical techniques to nonlocal operators

Insights into relativistic quantum bound states

Abstract

The spinless Salpeter equation can be regarded as the eigenvalue equation of a Hamiltonian that involves the relativistic kinetic energy and therefore is, in general, a nonlocal operator. Accordingly, it is hard to find solutions of this bound-state equation by exclusively analytic means. Nevertheless, a lot of tools enables us to constrain the resulting bound-state spectra rigorously. We illustrate some of these techniques for the example of the Hulth\'en potential.