The classical source-free electric field is a polar transverse-vector field, but the classical magnetic field is an axial transverse-vector field. A derivative-related linear transformation (which is its own inverse) of the classical axial magnetic field in fact produces an alternate polar transverse-vector representation of the classical magnetic field. The classical source-free complex-valued electromagnetic polar transverse-vector field whose real part is the classical source-free polar electric field, and whose imaginary part is the alternate polar representation of the classical source-free magnetic field, turns out to satisfy the time-dependent Schroedinger equation whose Hamiltonian operator is that of the free photon. That classical source-free complex-valued electromagnetic polar transverse-vector field can, moreover, be slightly linearly modified to become the normalized wave function of the free photon.