Coulomb-oscillator duality in spaces of constant curvature
Coulomb-oscillator duality in spaces of constant curvature
In this paper we construct generalizations to spheres of the well-known Levi-Civita, Kustaanheimo–Steifel, and Hurwitz regularizing transformations in Euclidean spaces of dimensions two, three, and five. The corresponding classical and quantum mechanical analogs of the Kepler–Coulomb problem on these spheres are discussed.