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The Coulomb-Oscillator Relation on n-Dimensional Spheres and Hyperboloids
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abstract
In this paper we establish a relation between Coulomb and oscillator systems on $n$-dimensional spheres and hyperboloids for $n\geq 2$. We show that, as in Euclidean space, the quasiradial equation for the $n+1$ dimensional Coulomb problem coincides with the $2n$-dimensional quasiradial oscillator equation on spheres and hyperboloids. Using the solution of the Schr\"odinger equation for the oscillator system, we construct the energy spectrum and wave functions for the Coulomb problem.
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Generalized MICZ-Kepler systems on three-dimensional sphere and hyperboloid
Curved-space analogs of the generalized MICZ-Kepler system on S³ and the 3D hyperboloid are solved exactly, with two-quantum-number spectra and normalized wavefunctions.
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