ABSTRACT
We will start with a short historical account of the development of the spherical harmonics. Laplace’s equation in a sphere was solved by Bernoulli’s separation method in §4.3.3 and §8.10. The spherical harmonics are the angular portion (θ and φ portions of the spherical coordinates) of a set of solutions of Laplace’s equation. These harmonics are useful in many theoretical and physical applications, namely, in physics, seismology, geodesy, spectral analysis, magnetic fields, quantum mechanics and others. A detailed account of various approaches to spherical harmonics can be found in Courant and Hilbert [1968] and MacRobert [1967].
