  It is shown that the magnetic force between two classical point charges, each
undergoing relativistic circulatory motion of small radius compared to the
separation between their centers of circulation, and assuming a time-symmetric
electromagnetic interaction, is modulated by a factor that behaves similarly to
the Schr\"odinger wavefunction. The modulation solves an equation formally
identical to the time-dependent free-particle Schr\"odinger equation, apart
from a factor of two on the partial time derivative term. Separating variables
and considering motion in a time-independent potential obtains that the
modulation also satisfies an equation formally similar to the time-independent
Schro\"dinger equation. Using a formula for relativistic rest energy advanced
by Osiak, the time-independent Schr\"odinger equation is solved exactly by the
resulting modulation function. A simple interpretation for the quantum
mechanical wavefunction is proposed.
