Effective photon mass and exact translating quantum relativistic structures

TL;DR

This paper develops exact solutions to the Klein-Gordon equation in specific electromagnetic fields, revealing new quantum relativistic structures with potential localization effects, and analyzes their stability.

Contribution

It introduces a novel approach based on a variation of the Volkov solution to find exact solutions for charged particles in relativistic electromagnetic fields.

Findings

Exact solutions to the Klein-Gordon equation are obtained.

New quantum structures exhibit radial localization effects.

Solutions are stable under numerical simulations.

Abstract

Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can reveal a localization in the radial direction perpendicular to the wave packet propagation, thanks to a non-vanishing scalar potential. The external electromagnetic field, the particle current density and the charge density are determined. The stability analysis of the solutions is performed by means of numerical simulations. The results are useful for the description of a charged quantum test particle in the relativistic regime, provided spin effects are not decisive.