Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid

Details Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid

2008-03-14

arxiv.org/abs/0803.2117v1

Physics

Quantum Physics

11 pages, 5 figures

Scientific paper

10.1088/1751-8113/41/25/255201

A class of quantum superintegrable Hamiltonians defined on a two-dimensional hyperboloid is considered together with a set of intertwining operators connecting them. It is shown that such intertwining operators close a su(2,1) Lie algebra and determine the Hamiltonians through the Casimir operators. By means of discrete symmetries a broader set of operators is obtained closing a so(4,2) algebra. The physical states corresponding to the discrete spectrum of bound states as well as the degeneration are characterized in terms of unitary representations of su(2,1) and so(4,2).

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