The Scale Factors are , and the separation functions are , , , given a Stäckel Determinant of . The Laplacian is

(1) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

(9) |

(10) |

(11) |

(12) |

(13) |

(14) |

**References**

Arfken, G. ``Parabolic Coordinates
.'' §2.12 in
*Mathematical Methods for Physicists, 2nd ed.* Orlando, FL: Academic Press, pp. 109-111, 1970.

Morse, P. M. and Feshbach, H. *Methods of Theoretical Physics, Part I.* New York:
McGraw-Hill, pp. 514-515 and 660, 1953.

© 1996-9

1999-05-25