Superintegrable Systems in Darboux spaces

Details Superintegrable Systems in Darboux spaces Superintegrable Systems in Darboux spaces

2003-07-18

arxiv.org/abs/math-ph/0307039v1

J. Math. Phys. 44 (2003) 5811-5848

Physics

Mathematical Physics

Scientific paper

10.1063/1.1619580

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

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