As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in oblate spheroidal coordinates.
Helmholtz Differential Equation--Oblate Spheroidal Coordinates
See also
Helmholtz Differential Equation, Oblate Spheroidal CoordinatesExplore with Wolfram|Alpha
References
Arfken, G. "Oblate Spheroidal Coordinates
." §2.11 in Mathematical
Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 107-109,
1970.Byerly, W. E. An
Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal
Harmonics, with Applications to Problems in Mathematical Physics. New York:
Dover, pp. 242 and 245-247, 1959.Moon, P. and Spencer, D. E.
Field
Theory Handbook, Including Coordinate Systems, Differential Equations, and Their
Solutions, 2nd ed. New York: Springer-Verlag, pp. 33-34, 1988.Morse,
P. M. and Feshbach, H. Methods
of Theoretical Physics, Part I. New York: McGraw-Hill, p. 662, 1953.
Cite this as:
Weisstein, Eric W. "Helmholtz Differential Equation--Oblate Spheroidal Coordinates." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HelmholtzDifferentialEquationOblateSpheroidalCoordinates.html