Algebraic properties of three-four dimensional anisotropic oscillator potentials through Hamiltonian chains

2015/11/04 by Y. Tanoudis, Yannis Tanoudis, Tanoudis, Yannis
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.1511.01326

29 pages

arxiv created 2015/11/04 · openalex publication_date 2015/11/04 · arxiv updated 2015/11/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this work the notion of Hamiltonian chain is presented as applied to anisotropic oscillator potentials especially defined on three and four dimensional Euclidean spaces. A Hamiltonian chain is a sequence of superintegrable Hamiltonians which, in addition, constitute integrals of motion of a new superintegrable system. Along with the Poisson algebras the quantum counterparts of the chain is given as well as the eigenvalues of each member of the chain. The method can be extended to cover n dimensional cases.

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