Superintegrable quantum u(3)--systems and higher rank factorizations

Details Superintegrable quantum u(3)--systems and higher rank factorizations Superintegrable quantum u(3)--systems and higher rank factorizations

2006-01-31

arxiv.org/abs/math-ph/0601067v1

Physics

Mathematical Physics

20 pages, 4 figures

Scientific paper

10.1063/1.2191360

A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant intertwining operators we arrive at a $so(6)$ dynamical algebra and its Hamiltonian hierarchies. We pay attention to those associated to certain unitary irreducible representations that can be displayed by means of three-dimensional polyhedral lattices. We also discuss the role of superpotentials in this new context.

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