Models of quadratic quantum algebras and their relation to classical superintegrable systems

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Models of quadratic quantum algebras and their relation to classical superintegrable systems

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Kalnins, E.G.

Miller Jr., W.

Post, Sarah

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2008-09-12

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Conference Paper

Abstract

We show how to construct realizations (models) of quadratic algebras for 2 dimensional second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.

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superintegrability

Hamiltonian systems

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Kalnins, E.G.; Miller Jr., W.; Post, Sarah. (2008). Models of quadratic quantum algebras and their relation to classical superintegrable systems. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/43088.

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