Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid
Quantum Physics
2009-11-13 v1
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).
Cite
@article{arxiv.0803.2117,
title = {Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid},
author = {J. A. Calzada and S. Kuru and J. Negro and M. A. del Olmo},
journal= {arXiv preprint arXiv:0803.2117},
year = {2009}
}
Comments
11 pages, 5 figures