Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid

2008/03/14 by Juan Antonio Aparicio Calzada, J. A. Calzada, Ş. Kuru +3 · 4 citations
Physics and Astronomy · #Advanced Fiber Laser Technologies #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #quant-ph

paper · pdf · doi:10.1088/1751-8113/41/25/255201

11 pages, 5 figures

arxiv created 2008/03/14 · openalex publication_date 2008/05/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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).

Cited by

• An infinite family of superintegrable systems from higher order ladder operators and supersymmetry
• Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions
• Superintegrability and higher order polynomial algebras
• Solution of second order supersymmetrical intertwining relations in Minkowski plane

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