Classical ladder operators, polynomial Poisson algebras, and classification of superintegrable systems

DOI10.1063/1.3676075zbMath1273.81075arXiv1109.4471OpenAlexW2052983749MaRDI QIDQ2853632

Ian Marquette

Publication date: 16 October 2013

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

Full work available at URL: https://arxiv.org/abs/1109.4471

zbMATH Keywords

deformation of Lissajous's figures

Mathematics Subject Classification ID

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) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Poisson algebras (17B63) Painlevé-type functions (33E17) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (10)

Two-dimensional superintegrable systems from operator algebras in one dimension ⋮ An affine Weyl group characterization of polynomial Heisenberg algebras ⋮ Doubly exotic \(N\)th-order superintegrable classical systems separating in Cartesian coordinates ⋮ Higher order supersymmetric truncated oscillators ⋮ Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator ⋮ \(N^{th}\)-order superintegrable systems separating in polar coordinates ⋮ Bi-Hamiltonian structure of the bi-dimensional superintegrable nonlinear isotonic oscillator ⋮ General Nth-order superintegrable systems separating in polar coordinates ⋮ New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates ⋮ On superintegrability of 3D axially-symmetric non-subgroup-type systems with magnetic fields

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