Spherical Harmonics – Solutions to the Angular Laplacian

In this video, I go over the actual spherical harmonics equations, which exclude the radial terms from the solid spherical harmonics I had derived earlier. The spherical harmonics can be combined into one function that contains all of the angular terms, thus essentially treating the sphere's radius as a constant. I also show how the spherical harmonics can be considered the solution of a modified Laplace equation, and hence a modified Laplace operator termed the angular Laplacian.

#math #sphericalharmonics #calculus #quantumphysics #laplace