Mathematical Methods in the Physical Sciences · Problem 7.16

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · wave-equation-spherical-bessel

Problem

Separate the wave equation in spherical coordinates, and show that the

\theta

\phi

solutions are the spherical harmonics

P_l^m(\cos\theta)e^{\pm im\phi}

and the

r

solutions are spherical Bessel functions

j_l(kr)

and

y_l(kr)

[Chapter 12, equations (17.4)].