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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 025, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.025 (Mi sigma151) 		 
This article is cited in 26 scientific papers (total in 26 papers)

Quantum Super-Integrable Systems as Exactly Solvable Models

Allan P. Fordy

Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Full-text PDF (215 kB) Citations (26)
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DOI: https://doi.org/10.3842/SIGMA.2007.025
URL: https://emis.mi.ras.ru/journals/SIGMA/2007/025
Abstract: We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are constructed through the action of the commuting operators. Finite dimensional representations of the quadratic algebras are thus constructed in a way analogous to that of the highest weight representations of Lie algebras.
Keywords: quantum integrability; super-integrability; exact solvability; Laplace–Beltrami.
Received: November 14, 2006; in final form February 5, 2007; Published online February 14, 2007
Bibliographic databases:
Document Type: Article
MSC: 35Q40; 70H06
Language: English
Citation: Allan P. Fordy, “Quantum Super-Integrable Systems as Exactly Solvable Models”, SIGMA, 3 (2007), 025, 10 pp.
Citation in format AMSBIB
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