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Symmetry, Integrability and Geometry: Methods and Applications, 2008, Volume 4, 046, 9 pp.
DOI: https://doi.org/10.3842/SIGMA.2008.046 (Mi sigma299) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Hamiltonian Systems Inspired by the Schrödinger Equation

Vasyl Kovalchuk, Jan Jerzy Slawianowski

Institute of Fundamental Technological Research, Polish Academy of Sciences, 21, Swiętokrzyska str., 00-049 Warsaw, Poland
Full-text PDF (189 kB) Citations (8)
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DOI: https://doi.org/10.3842/SIGMA.2008.046
Abstract: 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.
Keywords: Schrödinger equation; Hamiltonian systems on manifolds of scalar products; $n$-level quantum systems; scalar product as a dynamical variable; essential non-perturbative nonlinearity; conservation laws; $\mathrm{GL}(n,\mathbb C)$-invariance.
Received: October 30, 2007; in final form April 25, 2008; Published online May 27, 2008
Bibliographic databases:
Document Type: Article
MSC: 81P05; 81R05; 81Q99; 37J05; 15A04; 15A63; 15A90; 20G20
Language: English
Citation: Vasyl Kovalchuk, Jan Jerzy Slawianowski, “Hamiltonian Systems Inspired by the Schrödinger Equation”, SIGMA, 4 (2008), 046, 9 pp.
Citation in format AMSBIB
\Bibitem{KovSaw08}
\by Vasyl Kovalchuk, Jan Jerzy Slawianowski
\paper Hamiltonian Systems Inspired by the Schr\"odinger Equation
\jour SIGMA
\yr 2008
\vol 4
\papernumber 046
\totalpages 9
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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