Geodesic
Wigner function of a~relativistic particle in a~time-dependent linear potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 1, pp. 76-84

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We construct phase-space representations for a relativistic particle in both a constant and a time-dependent linear potential. We obtain explicit expressions for the Wigner distribution functions for these systems and find the correct nonrelativistic limit and free-particle limit for these functions. We derive the relativistic dynamical equation governing the time development of the Wigner distribution function and relativistic equation for the Wigner distribution function of stationary states and also calculate the amplitudes of transitions between energy states.
Keywords: relativistic particle, linear potential, Wigner function, dynamical equation. 
@article{TMF_2016_188_1_a4,
     author = {Sh. M. Nagiyev},
     title = {Wigner function of a~relativistic particle in a~time-dependent linear potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {76--84},
     publisher = {mathdoc},
     volume = {188},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_1_a4/}
}
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Sh. M. Nagiyev. Wigner function of a~relativistic particle in a~time-dependent linear potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 1, pp. 76-84. http://geodesic.mathdoc.fr/item/TMF_2016_188_1_a4/