Geodesic
Wigner distribution functions for a~relativistic linear oscillator
Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 3, pp. 410-425

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We construct the Wigner representation for a relativistic model of the linear harmonic oscillator governed by a finite-difference equation. We find Wigner functions for the stationary states, the thermodynamic equilibrium states, and the coherent states. We examine their nonrelativistic limits and the high and low temperature limits for the equilibrium states. We compute the mean values of the position and momentum coordinates for these Wigner functions. 
@article{TMF_1998_114_3_a6,
     author = {N. M. Atakishiyev and Sh. M. Nagiyev and K. B. Wolf},
     title = {Wigner distribution functions for a~relativistic linear oscillator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {410--425},
     publisher = {mathdoc},
     volume = {114},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_114_3_a6/}
}
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N. M. Atakishiyev; Sh. M. Nagiyev; K. B. Wolf. Wigner distribution functions for a~relativistic linear oscillator. Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 3, pp. 410-425. http://geodesic.mathdoc.fr/item/TMF_1998_114_3_a6/