Related papers: Dynamical symmetries of the anisotropic oscillator

Dynamical symmetries of the anisotropic oscillator

URL: http://arxiv.org/abs/2304.14306v1
Date: Thu, 27 Apr 2023 16:21:49 GMT
Title: Dynamical symmetries of the anisotropic oscillator
Authors: Akash Sinha, Aritra Ghosh, Bijan Bagchi
Abstract summary: We introduce a novel set of canonical transformations that map an $n$-dimensional anisotropic oscillator to the corresponding isotropic problem. The anisotropic oscillator is shown to possess the same number of conserved quantities as the isotropic oscillator, making it maximally superintegrable too.
Score: 8.228889210180268
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: It is well known that the Hamiltonian of an $n$-dimensional isotropic oscillator admits of an $SU(n)$ symmetry, making the system maximally superintegrable. However, the dynamical symmetries of the anisotropic oscillator are much more subtle. We introduce a novel set of canonical transformations that map an $n$-dimensional anisotropic oscillator to the corresponding isotropic problem. Interestingly, the anisotropic oscillator is shown to possess the same number of conserved quantities as the isotropic oscillator, making it maximally superintegrable too. The first integrals are explicitly calculated in the case of a two-dimensional anisotropic oscillator and remarkably, they admit closed form expressions.

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