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Models of Quadratic Algebras Generated by Superintegrable Systems in 2D

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arxiv 1104.0734 v1 pith:WFUWBKT3 submitted 2011-04-05 math-ph math.MPnlin.SI

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classification math-phmath.MPnlin.SI
keywords systemsalgebrasgeneratedmodelsquadraticsuperintegrableackelalmost
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In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of St\"ackel equivalent systems for both degenerate and nondegenerate systems. In almost all cases, the models can be used to determine the quantization of energy and eigenvalues for integrals associated with separation of variables in the original system.

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  1. The 2D Smorodinsky--Winternitz II system and the Laguerre--Heun algebra

    math-ph 2026-05 unverdicted novelty 5.0 of 10

    The symmetry algebra of the Smorodinsky-Winternitz II system is identified as the Laguerre-Heun algebra through explicit operators Y, W and their commutation relations.

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