Singular states of relativistic fermions in the field of a circularly polarized electromagnetic wave and constant magnetic field

TL;DR

This paper presents exact localized solutions to Dirac's equation for relativistic fermions in combined electromagnetic and magnetic fields, identifying singular states with practical separation methods and defining their key parameters.

Contribution

It introduces novel exact solutions for relativistic fermions in combined fields, including singular states with close energy eigenvalues and phase matching separation techniques.

Findings

Identification of singular solutions with close energy eigenvalues

Development of phase matching method for state separation

Definition of characteristic parameters of singular states

Abstract

Dirac's equation in the field of a circularly polarized electromagnetic wave and constant magnetic field has exact localized non-stationary solutions. The solutions corresponds relativistic fermions only. Among them singular solutions with energy eigenvalues close to each other are found. The solutions are most practicable and can be separated by means of the phase matching between the momentum of the electromagnetic wave and spinor. Characteristic parameters of the singular states are defined.