Adding Potentials to Superintegrable Systems with Symmetry

Autor:	Fordy, Allan P., Huang, Qing
Rok vydání:	2020
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical Physics 17B63 37J15 37J35 70G45 70G65 70H06
Druh dokumentu:	Working Paper
DOI:	10.1098/rspa.2020.0800
Popis:	In previous work, we have considered Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. Previously our Hamiltonians have represented free motion, but here we consider the problem of adding potential functions in the presence of symmetry. Separable potentials in the 3 dimensional space reduce to 3 or 4 parameter potentials for Darboux-Koenigs Hamiltonians. Other 3D coordinate systems reveal connections between Darboux-Koenigs and other well known super-integrable Hamiltonians, such as the Kepler problem and isotropic oscillator. Comment: 22 pages, 3 tables. arXiv admin note: text overlap with arXiv:1910.08836
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.11653 Zobrazit plný text záznamu View this record from Arxiv