On the generalization of classical Zernike system

2022/08/10 by Cezary Gonera, Gonera, Cezary, Joanna Gonera +3 · 2 citations
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2208.05289

openalex publication_date 2022/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the results obtained recently (Nonlinearity \underline36 (2023), 1143) by providing a very simple proof of the superintegrability of the Hamiltonian H=p ²+F(q⋅p), q, p∈ℝ², for any analytic function F. The additional integral of motion is constructed explicitly and shown to reduce to a polynomial in canonical variables for polynomial F. The generalization to the case q, p∈ ℝⁿ is sketched.

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• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Two-dimensional classical superintegrable systems: polynomial algebra of integrals

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