The Coulomb-oscillator relation on n-dimensional spheres and hyperboloids

We establish a relation between Coulomb and oscillator systems on n-dimensional spheres and hyperboloids for n greater than or equal to 2. We show that, as in Euclidean space, the quasiradial equation for the (n + l)-dimensional Coulomb problem coincides with the 2n-dimensional quasiradial oscillator equation on spheres and hyperboloids. Using the solution of the Schrodinger equation for the oscillator system, we construct the energy spectrum and wave functions for the Coulomb problem. (C) 2002 MAIK "Nauka/Interperiodica".