General quantum-mechanical solution for twisted electrons in a uniform magnetic field

Relativistic quantum-mechanical description of twisted paraxial electron and photon beams

The analysis of twisted (vortex) paraxial photons and electrons is fulfilled in the framework of relativistic quantum mechanics. The use of the Foldy-Wouthuysen representation radically simplifies a description of relativistic electrons and clarifies fundamental properties of twisted particles. It is demonstrated that the twisted photon defined by the Laguerre-Gauss wave function is luminal. Its apparent subluminality takes place because the photon energy is contributed by the hidden transversal motion while the average transversal momentum vanishes. Nevertheless, the Laguerre-Gauss photon can…

Production of twisted particles in magnetic fields

The use of a (quasi)uniform magnetic field opens new possibilities for a production of twisted particles having orbital angular momenta. Quantum states suitable for a production of charged particles in a uniform magnetic field are determined. The particle penetration from a solenoid to vacuum or another solenoid is analyzed in detail. Experiments allowing one successful discoveries of twisted positrons and positroniums are developed. We find a new effect of increasing a uncertainty of phase of the particle rotation with the distance passed by the particle in the solenoid. This effect leads to …

对称性破缺的均匀磁场中的扭曲带电粒子

Twisted charged particles in the uniform magnetic field with broken symmetry

本文针对轴向对称性破缺均匀磁场中的非零 OAM 扭曲带电粒子，推广 Laguerre-Gauss 态并建立解析框架，揭示对称性破缺对 OAM 投影及态性质的影响。

Exact quantum-mechanical equations for particle beams

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.

Equivalence principle in context of large uniform acceleration - a quantum mechanical perspective

We study the effect of large acceleration of an uniformly accelerated frame on the validity of weak equivalence principle. Specifically we demonstrate how the behaviour of free quantum particle, as observed by an observer with large uniform acceleration, completely changes from that of a quantum particle emmarsed in a uniform gravitational field. We also extend our analysis to the simplest noncommutative space scenario to show that while spatial noncommutativity does not affect the quantum particle in a gravitational field, it does alter the energy eigenvalues of a quantum particle as seen fro…

Uncertainty relation for the position of an electron in a uniform magnetic field from quantum estimation theory

We investigate the uncertainty relation for estimating the position of one electron in a uniform magnetic field in the framework of the quantum estimation theory. Two kinds of momenta, canonical one and mechanical one, are used to generate a shift in the position of the electron. We first consider pure state models whose wave function is in the ground state with zero angular momentum. The model generated by the two-commuting canonical momenta becomes the quasi-classical model, in which the symmetric logarithmic derivative quantum Cramér-Rao bound is achievable. The model generated by the two n…