A system of Curvilinear Coordinates. There are several different conventions for the orientation and designation of
these coordinates. Arfken (1970) defines coordinates
such that

(1) | |||

(2) | |||

(3) |

In this work, following Morse and Feshbach (1953), the coordinates are used instead. In this convention, the traces of the coordinate surfaces of the -Plane are confocal Parabolas with a common axis. The curves open into the Negative

(4) | |||

(5) | |||

(6) |

where , , and . The Scale Factors are

(7) | |||

(8) | |||

(9) |

Laplace's Equation is

(10) |

**References**

Arfken, G. ``Parabolic Cylinder Coordinates (, , ).'' §2.8 in
*Mathematical Methods for Physicists, 2nd ed.* Orlando, FL: Academic Press, p. 97, 1970.

Morse, P. M. and Feshbach, H. *Methods of Theoretical Physics, Part I.* New York:
McGraw-Hill, p. 658, 1953.

© 1996-9

1999-05-26