## Abstract

The possibility that Schrödinger's equation with a given potential can separate in more than one coordinate system is intimately connected with the notion of superintegrability. Here we demonstrate, for nondegenerate potentials, how to establish a complete list of such potentials that are superintegrable on the complex 2-sphere, using essentially algebraic means. We classify all such potentials that admit a pair of second-order constants of motion. Here 'nondegenerate' means that the potentials depend on four independent parameters. The method of proof generalizes to other spaces and dimensions. We show for the 2-sphere that all these superintegrable systems possess the remarkable property that they correspond to quadratic algebras, and we work out the detailed structure relations and their quantum analogues.

Original language | English (US) |
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Pages (from-to) | 6791-6806 |

Number of pages | 16 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 33 |

Issue number | 38 |

DOIs | |

State | Published - Sep 29 2000 |