The Coulomb-oscillator relation on <Emphasis Type="Italic">n</Emphasis>-dimensional spheres and hyperboloids |
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| Authors: | E G Kalnins Jr" target="_blank">W MillerJr G S Pogosyan |
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| Institution: | (1) Department of Mathematics and Statistics, University of Waikato, Hamilton, New Zealand;(2) School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA;(3) International Center for Advanced Studies, Yerevan State University, ul. A. Manougian 1, 375049 Yerevan, Armenia;(4) Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia |
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| Abstract: | 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. |
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