Superintegrability on the two-dimensional hyperboloid

DOI10.1063/1.531951zbMath0895.58049OpenAlexW4239711133MaRDI QIDQ4379276

Willard jun. Miller, Ernest G. Kalnins, George S. Pogosyan

Publication date: 25 February 1998

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531951

zbMATH Keywords

separation of variablessuperintegrable systemstwo-dimensional hyperboloid

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (17)

Klein-Gordon equation with superintegrable systems: Kepler-Coulomb, harmonic oscillator, and hyperboloid ⋮ Superintegrability on the Dunkl oscillator model in three-dimensional spaces of constant curvature ⋮ Quantum superintegrable systems with quadratic integrals on a two dimensional manifold ⋮ The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature ⋮ Dynamical symmetries, bi-Hamiltonian structures, and superintegrable n=2 systems ⋮ Coulomb-oscillator duality in spaces of constant curvature ⋮ The super-separability of the three-body inverse-square Calogero system ⋮ The Casimir elements of the Racah algebra ⋮ Finite-dimensional modules of the universal Racah algebra and the universal additive DAHA of type \((C_1^\vee,C_1)\) ⋮ Massless geodesics in \(\text{AdS}_5\times Y(p,q)\) as a superintegrable system ⋮ Superintegrability in three-dimensional Euclidean space ⋮ Superintegrability on the two-dimensional hyperboloid. II ⋮ The universal enveloping algebra of sl2 and the Racah algebra ⋮ Superintegrability on \(N\)-dimensional curved spaces: central potentials, centrifugal terms and monopoles ⋮ Comment on “Dynamical systems and Poisson structures” [J. Math. Phys. 50, 112703 (2009)] ⋮ Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2 ⋮ Quantum phase space for the one-dimensional hydrogen atom on the hyperbola

Cites Work

• Orthogonal polynomials in two variables
• Families of Orthogonal and Biorthogonal Polynomials on theN-Sphere
• Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces
• Lie algebras for systems with mixed spectra. I. The scattering Pöschl–Teller potential
• Dynamical symmetries in a spherical geometry. I
• Some Hypergeometric Orthogonal Polynomials
• Hypergeometric Expansions of Heun Polynomials
• Group theory of the Smorodinsky–Winternitz system
• Separable coordinates, integrability and the Niven equations
• A new basis for the representations of the rotation group. Lamé and Heun polynomials
• Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions
• Enumeration of Potentials for Which One-Particle Schroedinger Equations Are Separable

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