Geodesic
Operator method for calculating $Q$ symbols and their relation to
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 2, pp. 207-224 Cet article a éte moissonné depuis la source Math-Net.Ru

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We propose a new method for calculating Husimi symbols of operators. In contrast to the standard method, it does not require using the anti-normal-ordering procedure. According to this method, the coordinate and momentum operators $\hat q$ and $\hat p$ are assigned other operators $\widehat X$ and $\widehat P$ satisfying the same commutation relations. We then find the result of acting with the $\widehat X$ and $\widehat P$ operators and also polynomials in these operators on the Husimi function. After the obtained expression is integrated over the phase space coordinates, the integrand becomes a Husimi function times the symbol of the operator chosen to act on that function. We explicitly evaluate the Husimi symbols for operators that are powers of $\widehat X$ or $\widehat P$.
Keywords: quantum mechanics, Husimi function, Wigner function, symplectic tomogram, scaling transformation. 
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     author = {V. A. Andreev and L. D. Davidovich and Milena D. Davidovich and Milo\v{s} D. Davidovic and V. I. Man'ko and M. A. Man'ko},
     title = {Operator method for calculating $Q$ symbols and their relation to},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {2014},
     volume = {179},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_179_2_a3/}
}
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V. A. Andreev; L. D. Davidovich; Milena D. Davidovich; Miloš D. Davidovic; V. I. Man'ko; M. A. Man'ko. Operator method for calculating $Q$ symbols and their relation to. Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 2, pp. 207-224. http://geodesic.mathdoc.fr/item/TMF_2014_179_2_a3/

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