Superintegrable Systems in Darboux spaces

Abstract

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.

References in corpus (3)

• Completeness of superintegrability in two-dimensional constant curvature spaces
• Superintegrability with third order invariants in quantum and classical mechanics
• Superintegrability in a two-dimensional space of non-constant curvature

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