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  is of the form

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.