Exact quantum-mechanical equations for particle beams

TL;DR

This paper derives exact quantum-mechanical equations for various particle beams, generalizing known paraxial equations in optics and particle physics, and analyzes their eigenfunctions.

Contribution

It introduces exact quantum equations for particle beams, extending previous paraxial approximations to more precise formulations.

Findings

Derived exact equations for photon, Dirac, and spin-1 particle beams

Generalized paraxial equations to exact quantum forms

Analyzed properties of eigenfunctions of these equations

Abstract

The exact quantum-mechanical equations for beams of free particles including photons and for beams of Dirac and spin-1 particles in a uniform magnetic field have been derived. These equations present the exact generalizations of the well-known paraxial equations in optics (exact Helmholtz equation for light beams) and particle physics and of the previously obtained paraxial equation for a Dirac particle in a uniform magnetic field. Some basic properties of exact wave eigenfunctions of particle beams have been determined.