  It has recently been shown that the classical electric and magnetic fields
which satisfy the source-free Maxwell equations can be linearly mapped into the
real and imaginary parts of a transverse-vector wave function which in
consequence satisfies the time-dependent Schroedinger equation whose
Hamiltonian operator is physically appropriate to the free photon. The
free-particle Klein-Gordon equation for scalar fields modestly extends the
classical wave equation via a mass term. It is physically untenable for
complex-valued wave functions, but has a sound nonnegative conserved-energy
functional when it is restricted to real-valued classical fields. Canonical
Hamiltonization and a further canonical transformation maps the real-valued
classical Klein-Gordon field and its canonical conjugate into the real and
imaginary parts of a scalar wave function (within a constant factor) which in
consequence satisfies the time-dependent Schroedinger equation whose
Hamiltonian operator has the natural correspondence-principle relativistic
square-root form for a free particle, with a mass that matches the Klein-Gordon
field theory's mass term. Quantization of the real-valued classical
Klein-Gordon field is thus second quantization of this natural
correspondence-principle first-quantized relativistic Schroedinger equation.
Source-free electromagnetism is treated in a parallel manner, but with the
classical scalar Klein-Gordon field replaced by a transverse vector potential
that satisfies the classical wave equation. This reproduces the previous
first-quantized results that were based on Maxwell's source-free electric and
magnetic field equations.
