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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| Дата: | 2008 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2008
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148984 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1489842019-02-20T01:25:48Z Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation Bahrami, S. Nasiri, S. 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. 2008 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148984 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Bahrami, S. Nasiri, S. |
| spellingShingle |
Bahrami, S. Nasiri, S. Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bahrami, S. Nasiri, S. |
| author_sort |
Bahrami, S. |
| title |
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_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_sort |
symmetry transformation in extended phase space: the harmonic oscillator in the husimi representation |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148984 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT bahramis symmetrytransformationinextendedphasespacetheharmonicoscillatorinthehusimirepresentation AT nasiris symmetrytransformationinextendedphasespacetheharmonicoscillatorinthehusimirepresentation |
| first_indexed |
2023-05-20T17:31:57Z |
| last_indexed |
2023-05-20T17:31:57Z |
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1796153512387674112 |