New solutions of relativistic wave equations in magnetic fields and longitudinal fields

TL;DR

This paper develops methods to explicitly describe and utilize the inherent arbitrariness in solutions of relativistic wave equations in specific electromagnetic fields, leading to new exact solutions with potential physical relevance.

Contribution

It introduces a transformation that reduces variables in relativistic wave equations, enabling the construction of novel exact solutions in magnetic and combined electric-magnetic fields.

Findings

New stationary solutions in magnetic fields

Nonstationary solutions in combined fields

Explicit description of solution arbitrariness

Abstract

We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation, which reduces effectively the number of variables in the initial equations. Then we use the corresponding representations to construct new sets of exact solutions, which may have a physical interest. Namely, we present new sets of stationary and nonstationary solutions in magnetic field and in some superpositions of electric and magnetic fields.