We establish a relation between Coulomb and oscillator systems on n-dimensional spheres and hyperboloids for n ≥ 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 Schrödinger equation for the oscillator system, we construct the energy spectrum and wave functions for the Coulomb problem.
Bibliographical noteFunding Information:
This work was finished while G. Pogosyan was visiting the Centro de Ciencias Físicas, Universidad Nacional Autónoma de México in Cuernavaca, Mexico. He is grateful to the Consejo Nacional de Ciencia y Tecnología(México) for a Cátedra Patrimonial Nivel II and the Russian Foundation for Basic Research (project no. 00-02-81023).