Electromagnetic waves, Inhomogeneous materials -- Electromagnetic properties
In many cases the electromagnetic modes of a sphere can be obtained exactly. Special simplifications occur when the conductivity, complex permittivity, and complex permeability vary only in the radial direction, and static and time dependent examples are discussed. With quadratic or Coulomblike permittivity variations, the wave functions resemble the quantum mechanical harmonic oscillator or hydrogen atom wave functions, and similar angular momentum operators are obtained.
Lee W. Casperson. Electromagnetic modes of an inhomogeneous sphere. Applied Optics, Volume 20, Number 15 (August 1981), pp. 2738-2741.