  We clarify some arguments concerning Jefimenko's equations, as a way of
constructing solutions to Maxwell's equations, for charge and current
satisfying the continuity equation. We then isolate a condition on
non-radiation in all inertial frames, which is intuitively reasonable for the
stability of an atomic system, and prove that the condition is equivalent to
the charge and current satisfying certain relations, including the wave
equations. Finally, we prove that with these relations, the energy in the
electromagnetic field is quantised and displays the properties of the Balmer
series.
