Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Theoretical Physics

The Wigner Functions for a Spin-1/2 Relativistic Particle in the Presence of Magnetic Field

Yang Yuan, Ke Li, J. H. Wang, Kai Ma

Published Aug 2, 2010• 7 citations
Publisher
DOI
10.1007/s10773-010-0262-0

Related papers

Finite Difference Time Evolution of the Quantum Wigner Function in the Presence of a Magnetic Field

Timothy Bergstresser, TOMAS B. MATERDEY

Bulletin of the American Physical Society•Mar 18, 2009•0 citations

Squeezed States, Gauge Invariance and Wigner Functions of a Particle in a Homogeneous Magnetic Field

M. G. Benedict, Attila Czirják, François Maria Peeters

Acta Physica Hungarica B) Quantum Electronics•Jan 1, 2004•2 citations

Wigner function for free relativistic particles

O. I. Zavialov, A. M. Malokostov

arXiv:hep-th/9812054•Theoretical and Mathematical Physics•Apr 1, 1999•13 citations

St¨uckelberg particle in external magnetic field. Nonrelativistic approximation. Exact solutions

Elena M. Ovsiyuk, A. Safronov, Alina V. Ivashkevich +1 more

The St¨uckelberg equation for a particle with two spin states, S = 1 and S = 0, is studied in the presence of an external uniform magnetic field. In relativistic case, the particle is described by an 11-component wave function. On the solutions of the equation, the operators of energy, the third projection of the total angular momentum, and the third projection of the linear momentum along the direction of the magnetic field are diagonalized. After separation of variables, we derive a system for 11 functions depending on one variable. We perform the nonrelativistic approximation in this system. For this we apply the known method of deriving nonrelativistic equations from relativistic ones, which is based on projective operators related to the matrix Γ0 of the relativistic equation. The nonrelativistic wave function turns out to be 4-dimensional. We derive the system for 4 functions. It is solved in terms of confluent hypergeometric functions. There arise three series of energy levels with corresponding solutions. This result agrees with that obtained for the relativistic St¨uckelberg equation.

Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences•Dec 20, 2022•1 citation

The Wigner function in the relativistic quantum mechanics

K. Kowalski, Jakub Rembieliński

arXiv:1903.08975•Annals of Physics•Oct 8, 2016•9 citations

Relativistic generalization of the Wigner function and its interpretation in the causal stochastic formulation of quantum mechanics

Peter Holland, Anastasios Kyprianidis, Z. Marić +1 more

We show how the causal interpretation provides a physical basis for the Wigner phase-space formulation of quantum mechanics by analyzing the case of a relativistic spin-zero particle in an external electromagnetic field. The Wigner function can be interpreted as both a generalized transformation and a field which defines a quantum potential in phase space. We also propose a Lorentz-vector distribution function which always associates positive probability densities with the real motions of particles and antiparticles in phase space.

Physical Review A•Jun 1, 1986•27 citations
The St¨uckelberg equation for a particle with two spin states, S = 1 and S = 0, is studied in the presence of an external uniform magnetic field. In relativistic case, the particle is described by an 11-component wave function. On the solutions of the equation, the operators of energy, the third projection of the total angular momentum, and the third projection of the linear momentum along the direction of the magnetic field are diagonalized. After separation of variables, we derive a system for 11 functions depending on one variable. We perform the nonrelativistic approximation in this system. For this we apply the known method of deriving nonrelativistic equations from relativistic ones, which is based on projective operators related to the matrix Γ0 of the relativistic equation. The nonrelativistic wave function turns out to be 4-dimensional. We derive the system for 4 functions. It is solved in terms of confluent hypergeometric functions. There arise three series of energy levels with corresponding solutions. This result agrees with that obtained for the relativistic St¨uckelberg equation.
We show how the causal interpretation provides a physical basis for the Wigner phase-space formulation of quantum mechanics by analyzing the case of a relativistic spin-zero particle in an external electromagnetic field. The Wigner function can be interpreted as both a generalized transformation and a field which defines a quantum potential in phase space. We also propose a Lorentz-vector distribution function which always associates positive probability densities with the real motions of particles and antiparticles in phase space.