Operator method for calculating $Q$ symbols and their relation to
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 2, pp. 207-224
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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.
@article{TMF_2014_179_2_a3,
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},
pages = {207--224},
publisher = {mathdoc},
volume = {179},
number = {2},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2014_179_2_a3/}
}
TY - JOUR AU - V. A. Andreev AU - L. D. Davidovich AU - Milena D. Davidovich AU - Miloš D. Davidovic AU - V. I. Man'ko AU - M. A. Man'ko TI - Operator method for calculating $Q$ symbols and their relation to JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2014 SP - 207 EP - 224 VL - 179 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2014_179_2_a3/ LA - ru ID - TMF_2014_179_2_a3 ER -
%0 Journal Article %A V. A. Andreev %A L. D. Davidovich %A Milena D. Davidovich %A Miloš D. Davidovic %A V. I. Man'ko %A M. A. Man'ko %T Operator method for calculating $Q$ symbols and their relation to %J Teoretičeskaâ i matematičeskaâ fizika %D 2014 %P 207-224 %V 179 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2014_179_2_a3/ %G ru %F TMF_2014_179_2_a3
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/