  It was pointed out in a previous paper that although neither the Klein-Gordon
equation nor the Dirac Hamiltonian produces sound solitary free-particle
relativistic quantum mechanics, the natural square-root relativistic
Hamiltonian for a nonzero-mass free particle does achieve this. Failures of the
Klein-Gordon and Dirac theories are reviewed: the solitary Dirac free particle
has, inter alia, an invariant speed well in excess of c and staggering
spontaneous Compton acceleration, but no pathologies whatsoever arise from the
square-root relativistic Hamiltonian. Dirac's key misapprehension of the
underlying four-vector character of the time-dependent,
configuration-representation Schroedinger equation for a solitary particle is
laid bare, as is the invalidity of the standard "proof" that the
nonrelativistic limit of the Dirac equation is the Pauli equation. Lorentz
boosts from the particle rest frame point uniquely to the square-root
Hamiltonian, but these don't exist for a massless particle. Instead, Maxwell's
equations are dissected in spatial Fourier transform to separate nondynamical
longitudinal from dynamical transverse field degrees of freedom. Upon their
decoupling in the absence of sources, the transverse field components are seen
to obey two identical time-dependent Schroedinger equations (owing to two
linear polarizations), which have the massless free-particle diagonalized
square-root Hamiltonian. Those fields are readily modified to conform to the
attributes of solitary-photon wave functions. The wave functions' relations to
the potentials in radiation gauge are also worked out. The exercise is then
repeated without the considerable benefit of the spatial Fourier transform.
