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Helmholtz Differential Equation--Spherical Coordinates

The Helmholtz differential equation in spherical coordinates is separable. In fact, it is separable under the more general condition that k^2 is of the form

k^2(r,theta,phi)=f(r)+(g(theta))/(r^2)+(h(phi))/(r^2sintheta)+k^('2).

See also

Helmholtz Differential Equation, Laplace's Equation--Spherical Coordinates, Spherical Coordinates, Spherical Harmonic

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References

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, p. 244, 1959.Moon, P. and Spencer, D. E. Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd ed. New York: Springer-Verlag, p. 27, 1988.Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 514 and 658, 1953.

Cite this as:

Weisstein, Eric W. "Helmholtz Differential Equation--Spherical Coordinates." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HelmholtzDifferentialEquationSphericalCoordinates.html

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