Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid

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).

11 pages, 5 figures

References in corpus (8)

• Two families of superintegrable and isospectral potentials in two dimensions
• Generalized Morse Potential: Symmetry and Satellite Potentials
• Intertwined isospectral potentials in an arbitrary dimension
• Factorizations of one dimensional classical systems
• Intertwined Hamiltonians in Two Dimensional Curved Spaces
• The Conformal Group SU(2,2) and Integrable Systems on a Lorentzian Hyperboloid
• Superintegrable quantum u(3)--systems and higher rank factorizations
• Pseudo-orthogonal groups and integrable dynamical systems in two dimensions

Cited by in corpus (8)

• Superintegrability and higher order polynomial algebras I
• An infinite family of superintegrable systems from higher order ladder operators and supersymmetry
• Polynomial algebras from $su(3)$ and the generic model on the two sphere
• The general Racah algebra as the symmetry algebra of generic systems on pseudo--spheres
• Intertwining Symmetry Algebras of Quantum Superintegrable Systems
• Demkov-Fradkin tensor for curved harmonic oscillators
• Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions
• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane