Geodesic
Wigner's quantum distribution function in spherical coordinates
Teoretičeskaâ i matematičeskaâ fizika, Tome 27 (1976) no. 3, pp. 418-424 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
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     year = {1976},
     volume = {27},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1976_27_3_a13/}
}
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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/

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