Geodesic
Wigner's quantum distribution function in spherical coordinates
Teoretičeskaâ i matematičeskaâ fizika, Tome 27 (1976) no. 3, pp. 418-424 
N. A. Denisova. Wigner's quantum distribution function in spherical coordinates. Teoretičeskaâ i matematičeskaâ fizika, Tome 27 (1976) no. 3, pp. 418-424. http://geodesic.mathdoc.fr/item/TMF_1976_27_3_a13/
@article{TMF_1976_27_3_a13,
     author = {N. A. Denisova},
     title = {Wigner's quantum distribution function in spherical coordinates},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {418--424},
     year = {1976},
     volume = {27},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1976_27_3_a13/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The possibility is examined of applying the general method for introducing quantum distribution functions (QDF) proposed by Moyal to the concrete system of dynamical spherical variables $\widehat{\varphi}$, $\widehat{\theta}$, $\widehat r$, $\widehat p_{\varphi}$, $\widehat p_{\theta}$, $\widehat p_r$. The Wigner quantum distribution fimction found in this way in spherical coordinates determines the state of a system of particles only if the system is spherically or cylindrically symmetric. The changes are pointed out which must be made in Moyal's expressions for the basis operators $\widehat{\varphi}$, $\widehat{\theta}$, $\widehat r$, $\widehat p_{\varphi}$, $\widehat p_{\theta}$, $\widehat p_r$ if the distribution in the phase space $\varphi$, $\theta$, $r$, $n\hbar$, $m\hbar$, $p_r$ is to describe the state of any system of particles.

[1] E. Wigner, Phys. Rev., 40 (1932), 749 | DOI | Zbl

[2] D. Judge, Nuovo Cim., 31 (1964), 332 | DOI | MR | Zbl

[3] D. I. Blokhintsev, Osnovy kvantovoi mekhaniki, «Vysshaya shkola», 1963 | MR

[4] J. E. Moyal, Proc. Cambr. Phil. Soc., 45 (1949), 99 | DOI | MR | Zbl

[5] P. Carruthers, M. Nieto, Rev. Mod. Phys., 40 (1968), 411 | DOI

[6] D. A. Kirzhnits, Polevye metody teorii mnogikh chastits, Atomizdat, 1963

[7] N. F. Khiralla, SAN GSSR, 72 (1973), 557

[8] G. Korn, T. Korn, Spravochnik po matematike, «Nauka», 1966 | Zbl

[9] A. A. Vlasov, Statisticheskie funktsii raspredeleniya, «Nauka», 1966 | MR | Zbl

[10] A. I. Baz, Ya. B. Zeldovich, A. M. Perelomov, Rasseyanie, reaktsii i raspady v nerelyativistskoi kvantovoi mekhanike, «Nauka», 1971 | Zbl

[11] Yu. L. Klimontovich, DAN SSSR, 108 (1956), 1033 | Zbl

[12] N. A. Denisova, V. L. Konkov, TMF, 22 (1975), 64