Analytical solution of the relativistic Coulomb problem with a hard core interaction for a one-dimensional spinless Salpeter equation

TL;DR

This paper derives an analytical solution for a one-dimensional relativistic quantum system involving a Coulomb potential with a hard core, providing insights into bound states under relativistic conditions.

Contribution

It presents the first analytical solution to the relativistic Coulomb problem with a hard core in one dimension within the spinless Salpeter framework.

Findings

Analytical expressions for energy eigenvalues and wavefunctions

Bound state conditions with hard core interaction

Extension of non-relativistic Coulomb solutions to relativistic regime

Abstract

In this paper, we construct an analytical solution of the one-dimensional spinless Salpeter equation with a Coulomb potential supplemented by a hard core interaction, which keeps the particle in the x positive region.