Bound states of the Klein-Gordon equation in the presence of short-range potentials

TL;DR

This paper analytically solves the Klein-Gordon equation with a cusp potential to find bound states, including antiparticle states, providing insights into relativistic quantum systems with short-range potentials.

Contribution

It presents an exact solution for bound states of the Klein-Gordon equation in a cusp potential, highlighting antiparticle bound states, which is a novel analytical approach.

Findings

Derived explicit bound state solutions for the Klein-Gordon equation

Identified antiparticle bound states in the potential

Enhanced understanding of relativistic quantum bound states

Abstract

We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.