Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols
Само за регистроване кориснике
2014
Аутори
Andreev, Vladimir A.Davidović, Ljubica D.
Davidović, Milena
Davidović, Milos D.
Man'ko, V. I.
Manko, M. A.
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
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.
Кључне речи:
quantum mechanics / Husimi function / Wigner function / symplectic tomogram / scaling transformationИзвор:
Theoretical and Mathematical Physics, 2014, 179, 2, 559-573Издавач:
- Maik Nauka Publishing / Springer SBM
Финансирање / пројекти:
- Физичке импликације модификованог простор-времена (RS-MESTD-Basic Research (BR or ON)-171031)
- Нови приступ проблемима заснивања квантне механике са аспекта примене у квантним технологијама и интерпретацијама сигнала различитог порекла (RS-MESTD-Basic Research (BR or ON)-171028)
- Russian Foundation for Basic Research 11-02-01269
- Russian Foundation for Basic Research 10-02-00312
- Russian Foundation for Basic Research 11-02-00456
DOI: 10.1007/s11232-014-0162-1
ISSN: 0040-5779
WoS: 000337055200004
Scopus: 2-s2.0-84927604217
Колекције
Институција/група
GraFarTY - 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 . .