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arXiv · 0803.2117

Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid

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

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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J. A. Calzada, S. Kuru, J. Negro, M. A. del Olmo. 2008-03-14. Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid. https://doi.org/10.1088/1751-8113/41/25/255201

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