Superintegrable Lissajous systems on the sphere

2014/04/28 by Juan Antonio Aparicio Calzada, J. A. Calzada, Ş. Kuru +4
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1404.7064

16 pages, 3 figures. Submitted

arxiv created 2014/04/28 · openalex publication_date 2014/04/28 · arxiv updated 2014/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A kind of systems on the sphere, whose trajectories are similar to the Lissajous curves, are studied by means of one example. The symmetries are constructed following a unified and straightforward procedure for both the quantum and the classical versions of the model. In the quantum case it is stressed how the symmetries give the degeneracy of each energy level. In the classical case it is shown how the constants of motion supply the orbits, the motion and the frequencies in a natural way.

Citations

• Polynomial symmetries of spherical Lissajous systems

Related

• Polynomial symmetries of spherical Lissajous systems
• Equivalence between Type I Liouville dynamical systems in the plane and the sphere
• The Bannai-Ito algebra and a superintegrable system with reflections on the 2-sphere
• Classical Trajectories for two Ring-Shaped Potentials
• Classical Dynamical Symmetries and Geometry of Trajectories