Exact quantum-mechanical equations for particle beams
arXiv:2206.14901 · doi:10.1142/S0217732322500973
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.
arXiv comment4 pages
References in corpus (22)
- Theory and applications of free-electron vortex states
- Semiclassical Dynamics of Electron Wave Packet States with Phase Vortices
- Foldy-Wouthuysen transformation for relativistic particles in external fields
- Paraxial Light Beams with Angular Momentum
- The Foldy-Wouthuysen transformation
- Gaussian, Hermite-Gaussian, and Laguerre-Gaussian beams: A primer
- Position and spin in relativistic quantum mechanics
- General properties of the Foldy-Wouthuysen transformation and applicability of the corrected original Foldy-Wouthuysen method
- Relativistic quantum dynamics of twisted electron beams in arbitrary electric and magnetic fields
- Manipulating twisted electron beams
- Relativistic vortex electrons: paraxial versus non-paraxial regimes
- High-precision description and new properties of a spin-1 particle in a magnetic field
- Hamilton Operator and the Semiclassical Limit for Scalar Particles in an Electromagnetic Field
- Relativistic quantum-mechanical description of twisted paraxial electron and photon beams
- Electric quadrupole moment and the tensor magnetic polarizability of twisted electrons and a potential for their measurements
- General quantum-mechanical solution for twisted electrons in a uniform magnetic field
- Connection Between Wave Functions in the Dirac and Foldy-Wouthuysen Representations
- Exact solution of Helmholtz equation for the case of non-paraxial Gaussian beams
- Paraxial wave function and Gouy phase for a relativistic electron in a uniform magnetic field
- Dynamical enhancement of nonparaxial effects in the electromagnetic field of a vortex electron
- Dynamic structure factors of a strongly interacting Fermi superfluid near an orbital Feshbach resonance across the phase transition from BCS to Sarma superfluid
- Zitterbewegung of massless particles