### Abstract

We develop a calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schrödinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space. The infinite-order calculus exhibits structure not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. Among the simple consequences of the calculus is that one can generate algorithmically a canonical basis for the space. Similarly, we can develop a calculus for conformal symmetries of the time-dependent Schrödinger equation if it admits R separation in some coordinate system. This leads to energy-shifting symmetries.

Original language | English (US) |
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Pages (from-to) | 1756-1763 |

Number of pages | 8 |

Journal | Physics of Atomic Nuclei |

Volume | 68 |

Issue number | 10 |

DOIs | |

State | Published - Nov 7 2005 |

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## Cite this

*Physics of Atomic Nuclei*,

*68*(10), 1756-1763. https://doi.org/10.1134/1.2121926