### Abstract

A list of orthogonal coordinate systems which permit R-separation of the wave equation ψ_{tt}-Δ_{2}ψ = O is presented. All such coordinate systems whose coordinate curves are cyclides or their degenerate forms are given. In each case the coordinates and separation equations are computed. The two basis operators associated with each coordinate system are also presented as symmetric second order operators in the enveloping algebra of the conformal group O(3,2).

Original language | English (US) |
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Pages (from-to) | 331-355 |

Number of pages | 25 |

Journal | Journal of Mathematical Physics |

Volume | 17 |

Issue number | 3 |

DOIs | |

State | Published - 1975 |

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## Cite this

Kalnins, E. G., & Miller, W. (1975). Lie theory and separation of variables. 9. Orthogonal R-separable coordinate systems for the wave equation ψ

_{tt}-Δ_{2}ψ = O.*Journal of Mathematical Physics*,*17*(3), 331-355. https://doi.org/10.1063/1.522900