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Quantum Potential and Symmetries in Extended Phase Space
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space representation followed by the generalization of this concept to ext...
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Інститут математики НАН України
2006
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/146105 |
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irk-123456789-1461052019-02-08T01:23:16Z Quantum Potential and Symmetries in Extended Phase Space Nasiri, S. The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space representation followed by the generalization of this concept to extended phase space. It is shown that there exists an extended canonical transformation that removes the expression for the quantum potential in the dynamical equation. The situation, mathematically, is similar to disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates that changes the physical potential to an effective one. The representation where the quantum potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form, is one in which the dynamical equation turns out to be the Wigner equation. 2006 Article Quantum Potential and Symmetries in Extended Phase Space / S. Nasiri // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 31 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81S30 http://dspace.nbuv.gov.ua/handle/123456789/146105 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| language |
English |
| description |
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space representation followed by the generalization of this concept to extended phase space. It is shown that there exists an extended canonical transformation that removes the expression for the quantum potential in the dynamical equation. The situation, mathematically, is similar to disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates that changes the physical potential to an effective one. The representation where the quantum potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form, is one in which the dynamical equation turns out to be the Wigner equation. |
| format |
Article |
| author |
Nasiri, S. |
| spellingShingle |
Nasiri, S. Quantum Potential and Symmetries in Extended Phase Space Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Nasiri, S. |
| author_sort |
Nasiri, S. |
| title |
Quantum Potential and Symmetries in Extended Phase Space |
| title_short |
Quantum Potential and Symmetries in Extended Phase Space |
| title_full |
Quantum Potential and Symmetries in Extended Phase Space |
| title_fullStr |
Quantum Potential and Symmetries in Extended Phase Space |
| title_full_unstemmed |
Quantum Potential and Symmetries in Extended Phase Space |
| title_sort |
quantum potential and symmetries in extended phase space |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146105 |
| citation_txt |
Quantum Potential and Symmetries in Extended Phase Space / S. Nasiri // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 31 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT nasiris quantumpotentialandsymmetriesinextendedphasespace |
| first_indexed |
2023-05-20T17:23:50Z |
| last_indexed |
2023-05-20T17:23:50Z |
| _version_ |
1796153201385275392 |