Infinite families of superintegrable systems separable in subgroup coordinates

Abstract

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.

19 pages, 6 figures

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• The anisotropic oscillator on curved spaces: A new exactly solvable model
• Higher-order superintegrability of separable potentials with a new approach to the Post-Winternitz system
• Superintegrable systems with spin and second-order integrals of motion
• Superintegrable deformations of superintegrable systems : Quadratic superintegrability and higher-order superintegrability
• Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
• Quantum, classical symmetries and action-angle variables by factorization of superintegrable systems
• General Nth order integrals of the motion
• Demkov-Fradkin tensor for curved harmonic oscillators
• Superintegrable families of magnetic monopoles with non-radial potential in curved background
• Extensions of natural Hamiltonians
• Superintegrability of the Post-Winternitz system on spherical and hyperbolic spaces