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Dynamical symmetries for superintegrable quantum systems

J. A. Calzada·J. Negro·M. A. del Olmo
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Abstract

We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are obtained by generalizing the techniques of factorization of one-dimensional systems. We firstly obtain a pair of noncommuting Lie algebras $su(2)$ that originate the algebra $so(4)$. By considering three spherical coordinate systems we get the algebra $u(3)$ that can be enlarged by `reflexions' to $so(6)$. The bounded eigenstates of the Hamiltonian hierarchies are associated to the irreducible unitary representations of these dynamical algebras.

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J. A. Calzada, J. Negro, M. A. del Olmo. 2006-01-31. Dynamical symmetries for superintegrable quantum systems. https://doi.org/10.1134/s1063778807030088

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