In Cylindrical Coordinates, the Scale Factors are , ,
and the separation functions are , , , so the Stäckel Determinant is 1. Attempt Separation of Variables by writing

(1) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

The solution to the second part of (7) must not be sinusoidal at for a physical solution, so the
differential equation has a Positive separation constant

(8) |

(9) |

(10) |

(11) |

(12) |

(13) |

(14) |

Actually, the Helmholtz Differential Equation is separable for general of the form

(15) |

**References**

Morse, P. M. and Feshbach, H. *Methods of Theoretical Physics, Part I.* New York:
McGraw-Hill, pp. 514 and 656-657, 1953.

© 1996-9

1999-05-25