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 twodimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2space or on the complex 2sphere, via "coupling constant metamorphosis" (or equivalently, via Stäckel multiplier transformations). We present a table of the results.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 December 2003
 DOI:
 10.1063/1.1619580
 arXiv:
 arXiv:mathph/0307039
 Bibcode:
 2003JMP....44.5811K
 Keywords:

 02.30.Jr;
 Partial differential equations;
 Mathematical Physics;
 37K05 70H20
 EPrint:
 J. Math. Phys. 44 (2003) 58115848