Sinusoidal plane-wave solutions of the electromagnetic wave equation

Sinusoidal plane-wave solutions are particular solutions to the electromagnetic wave equation. The general solution of the electromagnetic wave equation in homogeneous, linear, time-independent media can be written as a linear superposition of plane-waves of different frequencies and polarizations. The treatment in this article is classical but, because of the generality of Maxwell's equations for electrodynamics, the treatment can be converted into the quantum mechanical treatment with only a reinterpretation of classical quantities (aside from the quantum mechanical treatment needed for charge and current densities). The reinterpretation is based on the theories of Max Planck and the interpretations by Albert Einstein of those theories and of other experiments. The quantum generalization of the classical treatment can be found in the articles on Photon polarization and Photon dynamics in the double-slit experiment.