Dynamical symmetries of the anisotropic oscillator

Autor:	Sinha, Akash, Ghosh, Aritra, Bagchi, Bijan
Rok vydání:	2023
Předmět:	Mathematical Physics High Energy Physics - Theory Physics - Classical Physics Quantum Physics
Druh dokumentu:	Working Paper
Popis:	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. Comment: Preliminary version, comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.14306 Zobrazit plný text záznamu View this record from Arxiv