Helmholtz Differential Equation--Parabolic Coordinates

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.

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