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Hamiltonian Systems Inspired by the Schrödinger Equation
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- Фізико-технічні та математичні науки
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Hamiltonian Systems Inspired by the Schrödinger Equation
Інший ID:
2000 Mathematics Subject Classification: 81P05; 81R05; 81Q99; 37J05; 15A04; 15A63; 15A90; 20G20
Посилання:
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.
Підтримка:
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.
Дата:
2008
Переглядів:
783
Завантажень:
237
Анотація:
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.
