### 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.

Original language | English (US) |
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Pages (from-to) | 1086-1094 |

Number of pages | 9 |

Journal | Physics of Atomic Nuclei |

Volume | 65 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2002 |

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## Cite this

Kalnins, E. G., Miller, W., & Pogosyan, G. S. (2002). The coulomb-oscillator relation on n-dimensional spheres and hyperboloids.

*Physics of Atomic Nuclei*,*65*(6), 1086-1094. https://doi.org/10.1134/1.1490116