Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation
In a previous work the concept of quantum potential is generalized into extended phase space (EPS) for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schrödinger quantum mechanics by an appropriate extended canonical transformation one can obtain the Wigner...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2008 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148984 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation / S. Bahrami, S. Nasiri // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862732532172193792 |
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| author | Bahrami, S. Nasiri, S. |
| author_facet | Bahrami, S. Nasiri, S. |
| citation_txt | Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation / S. Bahrami, S. Nasiri // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In a previous work the concept of quantum potential is generalized into extended phase space (EPS) for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schrödinger quantum mechanics by an appropriate extended canonical transformation one can obtain the Wigner representation of phase space quantum mechanics in which the quantum potential is removed from dynamical equation. In other words, one still has the form invariance of the ordinary Hamilton-Jacobi equation in this representation. The situation, mathematically, is similar to the disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates. Here we show that the Husimi representation is another possible representation where the quantum potential for the harmonic potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form. This happens when the parameter in the Husimi transformation assumes a specific value corresponding to Q-function.
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| first_indexed | 2025-12-07T19:31:49Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148984 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:31:49Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bahrami, S. Nasiri, S. 2019-02-19T12:41:22Z 2019-02-19T12:41:22Z 2008 Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation / S. Bahrami, S. Nasiri // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 18 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81S30 https://nasplib.isofts.kiev.ua/handle/123456789/148984 In a previous work the concept of quantum potential is generalized into extended phase space (EPS) for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schrödinger quantum mechanics by an appropriate extended canonical transformation one can obtain the Wigner representation of phase space quantum mechanics in which the quantum potential is removed from dynamical equation. In other words, one still has the form invariance of the ordinary Hamilton-Jacobi equation in this representation. The situation, mathematically, is similar to the disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates. Here we show that the Husimi representation is another possible representation where the quantum potential for the harmonic potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form. This happens when the parameter in the Husimi transformation assumes a specific value corresponding to Q-function. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). The financial support of Research Council of Zanjan University, Zanjan, Iran is appreciated. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation Article published earlier |
| spellingShingle | Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation Bahrami, S. Nasiri, S. |
| title | Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation |
| title_full | Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation |
| title_fullStr | Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation |
| title_full_unstemmed | Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation |
| title_short | Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation |
| title_sort | symmetry transformation in extended phase space: the harmonic oscillator in the husimi representation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148984 |
| work_keys_str_mv | AT bahramis symmetrytransformationinextendedphasespacetheharmonicoscillatorinthehusimirepresentation AT nasiris symmetrytransformationinextendedphasespacetheharmonicoscillatorinthehusimirepresentation |