Beyond Volkov: Solving the Second-Order Klein-Gordon Equation

TL;DR

This paper extends the analysis of scalar particles interacting with electromagnetic fields beyond the plane-wave approximation, providing exact solutions and insights into quantum dynamics in more complex field configurations.

Contribution

It introduces new exact solutions for the second-order Klein-Gordon equation in non-plane-wave electromagnetic fields, advancing understanding of quantum dynamics in realistic laser-matter interactions.

Findings

Derived exact solutions for scalar particles in non-plane-wave fields

Analyzed the validity of common approximations in complex field configurations

Explored quantum dynamics in standing wave backgrounds

Abstract

Whether monochromatic, pulsed, or even constant and crossed, the field used to describe the interaction of charged fermions with an intense laser beam is mainly assumed to be of plane-wave form. We consider a simple extension to plane-wave fields and consider a scalar particle in a non-lightlike, univariate and transverse propagating electromagnetic wave. The existence of some known exact solutions in this case allows us to analyse various proposed approximations in the literature as well as the plane wave model. The results also describe some of the quantum dynamics of a scalar particle in a standing wave background.