Superintegrable systems in Darboux spaces | Zendy

E. G. Kalnins | Zendy; J. M. Kress | Zendy; Willard Miller | Zendy; P. Winternitz | Zendy

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Superintegrable systems in Darboux spaces

Author(s) -

E. G. Kalnins,

J. M. Kress,

Willard Miller,

P. Winternitz

Publication year - 2003

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.1619580

Subject(s) - constant curvature , euclidean space , euclidean geometry , mathematical physics , coupling constant , curvature , hamiltonian (control theory) , mathematics , darboux integral , superintegrable hamiltonian system , quadratic equation , mathematical analysis , constant (computer programming) , multiplier (economics) , hamiltonian system , pure mathematics , physics , quantum mechanics , geometry , covariant hamiltonian field theory , mathematical optimization , computer science , economics , macroeconomics , programming language

Almost all research on superintegrable potentials concerns spaces of constantcurvature. In this paper we find by exhaustive calculation, all superintegrablepotentials in the four Darboux spaces of revolution that have at least twointegrals of motion quadratic in the momenta, in addition to the Hamiltonian.These are two-dimensional spaces of nonconstant curvature. It turns out thatall of these potentials are equivalent to superintegrable potentials in complexEuclidean 2-space or on the complex 2-sphere, via "coupling constantmetamorphosis" (or equivalently, via Staeckel multiplier transformations). Wepresent tables of the results

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