Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations
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2015
Authors
Andreev, Vladimir A.Davidović, Milena
Davidović, Ljubica D.
Davidović, Milos D.

Davidović, Dragomir M.
Article (Published version)

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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.
Keywords:
average values / Husimi function / polynomials / operators / scaling transform / uncertainty relationSource:
Physica Scripta, 2015, 90, 7Publisher:
- Institute of Physics Publishing
Funding / projects:
- Physical Implications of Modified Spacetime (RS-171031)
- A new approach to foundational problems of quantum mechanics related to applications in quantum technologies and interpretations of signals of various origins (RS-171028)
DOI: 10.1088/0031-8949/90/7/074023
ISSN: 0031-8949
WoS: 000357541800024
Scopus: 2-s2.0-84938531897
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GraFarTY - JOUR AU - Andreev, Vladimir A. AU - Davidović, Milena AU - Davidović, Ljubica D. AU - Davidović, Milos D. AU - Davidović, Dragomir M. PY - 2015 UR - https://grafar.grf.bg.ac.rs/handle/123456789/666 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. PB - Institute of Physics Publishing T2 - Physica Scripta T1 - Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations IS - 7 VL - 90 DO - 10.1088/0031-8949/90/7/074023 ER -
@article{ author = "Andreev, Vladimir A. and Davidović, Milena and Davidović, Ljubica D. and Davidović, Milos 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.", publisher = "Institute of Physics Publishing", journal = "Physica Scripta", title = "Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations", number = "7", volume = "90", doi = "10.1088/0031-8949/90/7/074023" }
Andreev, V. A., Davidović, M., Davidović, 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 Institute of Physics Publishing., 90(7). https://doi.org/10.1088/0031-8949/90/7/074023
Andreev VA, Davidović M, Davidović 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, Davidović, Ljubica D., Davidović, Milos 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 . .