TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milena
AU  - Davidović, Milos D.
AU  - Man'ko, V. I.
AU  - Manko, M. A.
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/645
AB  - 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 (q) over cap and (p) over cap are assigned other operators (X) over cap and (P) over cap satisfying the same commutation relations. We then find the result of acting with the (X) over cap and (P) over cap 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 (X) over cap or (P) over cap.
PB  - Maik Nauka Publishing / Springer SBM
T2  - Theoretical and Mathematical Physics
T1  - Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols
EP  - 573
IS  - 2
SP  - 559
VL  - 179
DO  - 10.1007/s11232-014-0162-1
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Ljubica D. and Davidović, Milena and Davidović, Milos D. and Man'ko, V. I. and Manko, M. A.",
year = "2014",
abstract = "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 (q) over cap and (p) over cap are assigned other operators (X) over cap and (P) over cap satisfying the same commutation relations. We then find the result of acting with the (X) over cap and (P) over cap 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 (X) over cap or (P) over cap.",
publisher = "Maik Nauka Publishing / Springer SBM",
journal = "Theoretical and Mathematical Physics",
title = "Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols",
pages = "573-559",
number = "2",
volume = "179",
doi = "10.1007/s11232-014-0162-1"
}

Andreev, V. A., Davidović, L. D., Davidović, M., Davidović, M. D., Man'ko, V. I.,& Manko, M. A.. (2014). Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols. in Theoretical and Mathematical Physics
Maik Nauka Publishing / Springer SBM., 179(2), 559-573.
https://doi.org/10.1007/s11232-014-0162-1

Andreev VA, Davidović LD, Davidović M, Davidović MD, Man'ko VI, Manko MA. Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols. in Theoretical and Mathematical Physics. 2014;179(2):559-573.
doi:10.1007/s11232-014-0162-1 .

Andreev, Vladimir A., Davidović, Ljubica D., Davidović, Milena, Davidović, Milos D., Man'ko, V. I., Manko, M. A., "Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols" in Theoretical and Mathematical Physics, 179, no. 2 (2014):559-573,
https://doi.org/10.1007/s11232-014-0162-1 . .