On ``spherical'' domains (the interior and exterior of a sphere, or in
a spherical shell) the completely general solution to the HHE can
therefore be written in *stationary* form as:

(13.38) |

or (for scattering theory, mostly) in the

(13.39) |

Inside a sphere, and must be zero. Outside a sphere, or in a spherical annulus, all the coefficients can be non-zero

[This should provoke deep thoughts about the fundamental significance of the Laplace equation. Are there any ``really'' stationary sources in the dynamical, covariant, universe? Do we expect to have a contribution to the zero frequency charge/current density distribution in any region of space? What would this correspond to?]

Robert G. Brown 2017-07-11