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 . .

TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Dragomir M.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milena
AU  - Man'ko, V. I.
AU  - Manko, M. A.
PY  - 2011
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/351
AB  - We consider the Husimi Q-functions, which are quantum quasiprobability distributions in the phase space, and investigate their transformation properties under a scale transformation (q, p) - gt (lambda q, lambda p). We prove a theorem that under this transformation, the Husimi function of a physical state is transformed into a function that is also a Husimi function of some physical state. Therefore, the scale transformation defines a positive map of density operators. We investigate the relation of Husimi functions to Wigner functions and symplectic tomograms and establish how they transform under the scale transformation. As an example, we consider the harmonic oscillator and show how its states transform under the scale transformation.
T2  - Theoretical and Mathematical Physics
T1  - A transformational property of the Husimi function and its relation to the Wigner function and symplectic tomograms
EP  - 368
IS  - 3
SP  - 356
VL  - 166
DO  - 10.1007/s11232-011-0028-8
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milena and Man'ko, V. I. and Manko, M. A.",
year = "2011",
abstract = "We consider the Husimi Q-functions, which are quantum quasiprobability distributions in the phase space, and investigate their transformation properties under a scale transformation (q, p) - gt (lambda q, lambda p). We prove a theorem that under this transformation, the Husimi function of a physical state is transformed into a function that is also a Husimi function of some physical state. Therefore, the scale transformation defines a positive map of density operators. We investigate the relation of Husimi functions to Wigner functions and symplectic tomograms and establish how they transform under the scale transformation. As an example, we consider the harmonic oscillator and show how its states transform under the scale transformation.",
journal = "Theoretical and Mathematical Physics",
title = "A transformational property of the Husimi function and its relation to the Wigner function and symplectic tomograms",
pages = "368-356",
number = "3",
volume = "166",
doi = "10.1007/s11232-011-0028-8"
}

Andreev, V. A., Davidović, D. M., Davidović, L. D., Davidović, M., Man'ko, V. I.,& Manko, M. A.. (2011). A transformational property of the Husimi function and its relation to the Wigner function and symplectic tomograms. in Theoretical and Mathematical Physics, 166(3), 356-368.
https://doi.org/10.1007/s11232-011-0028-8

Andreev VA, Davidović DM, Davidović LD, Davidović M, Man'ko VI, Manko MA. A transformational property of the Husimi function and its relation to the Wigner function and symplectic tomograms. in Theoretical and Mathematical Physics. 2011;166(3):356-368.
doi:10.1007/s11232-011-0028-8 .

Andreev, Vladimir A., Davidović, Dragomir M., Davidović, Ljubica D., Davidović, Milena, Man'ko, V. I., Manko, M. A., "A transformational property of the Husimi function and its relation to the Wigner function and symplectic tomograms" in Theoretical and Mathematical Physics, 166, no. 3 (2011):356-368,
https://doi.org/10.1007/s11232-011-0028-8 . .