The \(B_2\) harmonic oscillator with reflections and superintegrability

DOI10.3842/SIGMA.2023.025zbMath1515.81141arXiv2210.14180OpenAlexW4366988620MaRDI QIDQ6110580

Charles F. Dunkl

Publication date: 6 July 2023

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.14180

zbMATH Keywords

Jacobi polynomialsLaguerre polynomialsDunkl harmonic oscillatordihedral symmetrysuperintegrability

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (1)

The quantum harmonic oscillator with icosahedral symmetry and some explicit wavefunctions

Cites Work

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• Generalized Calogero-Moser systems from rational Cherednik algebras
• The Calogero-Sutherland model and generalized classical polynomials
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• Computing with differential-difference operators
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• An infinite family of solvable and integrable quantum systems on a plane
• Differential-Difference Operators Associated to Reflection Groups
• Orthogonal Polynomials of Several Variables
• Periodic orbits for an infinite family of classical superintegrable systems

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