Solutions of the Klein-Gordon equation in an infinite square-well potential with a moving wall

TL;DR

This paper derives exact solutions to the Klein-Gordon equation within an infinite square-well potential with a moving boundary, using a transformation to hyperbolic space, applicable to both massless and massive particles.

Contribution

It introduces a simple method using hyperbolic space transformation to find exact solutions for the Klein-Gordon equation with a moving wall.

Findings

Exact solutions for massless and massive cases

Method simplifies solving Klein-Gordon in dynamic boundaries

Applicable to relativistic quantum systems

Abstract

Employing a transformation to hyperbolic space, we derive in a simple way exact solutions for the Klein-Gordon equation in an infinite square-well potential with one boundary moving at constant velocity, for the massless as well as for the massive case.