Superintegrable quantum u(3)--systems and higher rank factorizations
arXiv:math-ph/0601067 · doi:10.1063/1.2191360
Abstract
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 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.
20 pages, 4 figures