TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Milena D.
AU  - Davidovic, Ljubica D.
AU  - Davidović, Miloš D.
AU  - Davidović, Dragomir M.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/643
AB  - We propose a new method for the derivation of Husimi symbols, for operators that are given in the form of products of an arbitrary number of coordinates, and momentum operators, in an arbitrary order. For such an operator, in the standard approach, one expresses coordinate and momentum operators as a linear combination of the creation and annihilation operators, and then uses the antinormal ordering to obtain the final form of the symbol. In our method, one obtains the Husimi symbol in a much more straightforward fashion, departing directly from operator explicit form without transforming it through creation and annihilation operators. With this method the mean values of some operators are found. It is shown how the Heisenberg and the Schrodinger-Robertson uncertainty relations, for position and momentum, are transformed under scale transformation (q; p) - GT (lambda q; lambda p). The physical sense of some states which can be constructed with this transformation is also discussed.
T2  - Physica Scripta
T1  - Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations
VL  - 90
IS  - 7
DO  - 10.1088/0031-8949/90/7/074023
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Milena D. and Davidovic, Ljubica D. and Davidović, Miloš D. and Davidović, Dragomir M.",
year = "2015",
abstract = "We propose a new method for the derivation of Husimi symbols, for operators that are given in the form of products of an arbitrary number of coordinates, and momentum operators, in an arbitrary order. For such an operator, in the standard approach, one expresses coordinate and momentum operators as a linear combination of the creation and annihilation operators, and then uses the antinormal ordering to obtain the final form of the symbol. In our method, one obtains the Husimi symbol in a much more straightforward fashion, departing directly from operator explicit form without transforming it through creation and annihilation operators. With this method the mean values of some operators are found. It is shown how the Heisenberg and the Schrodinger-Robertson uncertainty relations, for position and momentum, are transformed under scale transformation (q; p) - GT (lambda q; lambda p). The physical sense of some states which can be constructed with this transformation is also discussed.",
journal = "Physica Scripta",
title = "Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations",
volume = "90",
number = "7",
doi = "10.1088/0031-8949/90/7/074023"
}

Andreev, V. A., Davidović, M. D., Davidovic, L. D., Davidović, M. D.,& Davidović, D. M.. (2015). Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations. in Physica Scripta, 90(7).
https://doi.org/10.1088/0031-8949/90/7/074023

Andreev VA, Davidović MD, Davidovic LD, Davidović MD, Davidović DM. Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations. in Physica Scripta. 2015;90(7).
doi:10.1088/0031-8949/90/7/074023 .

Andreev, Vladimir A., Davidović, Milena D., Davidovic, Ljubica D., Davidović, Miloš D., Davidović, Dragomir M., "Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations" in Physica Scripta, 90, no. 7 (2015),
https://doi.org/10.1088/0031-8949/90/7/074023 . .