  We investigate the representations of the solutions to Maxwell's equations
based on the combination of hypercomplex function-theoretical methods with
quantum mechanical methods. Our approach provides us with a characterization
for the solutions to the time-harmonic Maxwell system in terms of series
expansions involving spherical harmonics resp. spherical monogenics. Also, a
thorough investigation for the series representation of the solutions in terms
of eigenfunctions of Landau operators that encode $n-$dimensional spinless
electrons is given.
  This new insight should lead to important investigations in the study of
regularity and hypo-ellipticity of the solutions to Schr\"odinger equations
with natural applications in relativistic quantum mechanics concerning massive
spinor fields.
