Hamiltonian Systems Inspired by the Schrödinger Equation
Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and conservation laws are obtained. Special ca...
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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/123456789/149037 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Hamiltonian Systems Inspired by the Schrödinger Equation / V. Kovalchuk, J.J. Slawianowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862532424442839040 |
|---|---|
| author | Kovalchuk, V. Slawianowski, J.J. |
| author_facet | Kovalchuk, V. Slawianowski, J.J. |
| citation_txt | Hamiltonian Systems Inspired by the Schrödinger Equation / V. Kovalchuk, J.J. Slawianowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and conservation laws are obtained. Special cases for the free evolution of the wave function with fixed G and the pure dynamics of G are calculated. The usual, first- and second-order modified Schrödinger equations are obtained.
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| first_indexed | 2025-11-24T04:40:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149037 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:40:18Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kovalchuk, V. Slawianowski, J.J. 2019-02-19T13:11:50Z 2019-02-19T13:11:50Z 2008 Hamiltonian Systems Inspired by the Schrödinger Equation / V. Kovalchuk, J.J. Slawianowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 16 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81P05; 81R05; 81Q99; 37J05; 15A04; 15A63; 15A90; 20G20 https://nasplib.isofts.kiev.ua/handle/123456789/149037 Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and conservation laws are obtained. Special cases for the free evolution of the wave function with fixed G and the pure dynamics of G are calculated. The usual, first- and second-order modified Schrödinger equations are obtained. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). This paper contains results obtained within the framework of the research project 501 018
 32/1992 financed from the Scientific Research Support Fund in 2007–2010. The authors are greatly indebted to the Ministry of Science and Higher Education for this financial support. The authors are also very grateful to the referees for their valuable remarks and comments concerning this article. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hamiltonian Systems Inspired by the Schrödinger Equation Article published earlier |
| spellingShingle | Hamiltonian Systems Inspired by the Schrödinger Equation Kovalchuk, V. Slawianowski, J.J. |
| title | Hamiltonian Systems Inspired by the Schrödinger Equation |
| title_full | Hamiltonian Systems Inspired by the Schrödinger Equation |
| title_fullStr | Hamiltonian Systems Inspired by the Schrödinger Equation |
| title_full_unstemmed | Hamiltonian Systems Inspired by the Schrödinger Equation |
| title_short | Hamiltonian Systems Inspired by the Schrödinger Equation |
| title_sort | hamiltonian systems inspired by the schrödinger equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149037 |
| work_keys_str_mv | AT kovalchukv hamiltoniansystemsinspiredbytheschrodingerequation AT slawianowskijj hamiltoniansystemsinspiredbytheschrodingerequation |