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Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 91, Number 2, Pages 207–216 (Mi tmf5573)  
This article is cited in 45 scientific papers (total in 45 papers)

Quadratic algebras and dynamics in curved spaces. I. Oscillator

Ya. I. Granovskii, A. S. Zhedanov, I. M. Lutsenko

Donetsk State University
Full-text PDF (980 kB) Citations (45)
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Abstract: The dynamical symmetry of a three-dimensional oscillator in a space of constant curvature is described by three operators formed from the components of the Fradkin–Higgs tensor and the generators of the quadratic Racah algebra $QR(3)$. This atgebra makes it possible to find all dynamical characteristics of the problem: the spectrum, degeneracy of the energy levels, and the overlap coefficients of the wave functions in different coordinate systems. The algebra that generates the spectrum is constructed and found to be the quadratic Jacobi algebra $QJ(3)$.
Received: 24.05.1991
English version:
Theoretical and Mathematical Physics, 1992, Volume 91, Issue 2, Pages 474–480
DOI: https://doi.org/10.1007/BF01018846
Bibliographic databases:
Language: Russian
Citation: Ya. I. Granovskii, A. S. Zhedanov, I. M. Lutsenko, “Quadratic algebras and dynamics in curved spaces. I. Oscillator”, TMF, 91:2 (1992), 207–216; Theoret. and Math. Phys., 91:2 (1992), 474–480
Citation in format AMSBIB
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\by Ya.~I.~Granovskii, A.~S.~Zhedanov, I.~M.~Lutsenko
\paper Quadratic algebras and dynamics in curved spaces.~I. Oscillator
\jour TMF
\yr 1992
\vol 91
\issue 2
\pages 207--216
\mathnet{http://mi.mathnet.ru/tmf5573}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1182536}
\transl
\jour Theoret. and Math. Phys.
\yr 1992
\vol 91
\issue 2
\pages 474--480
\crossref{https://doi.org/10.1007/BF01018846}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992KG55600003}
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  • https://www.mathnet.ru/eng/tmf/v91/i2/p207
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    This publication is cited in the following 45 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:77
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