  We present a unified view of the frequency dependence of the various
scattering processes involved when a neutral hydrogen atom interacts with a
monochromatic, linearly-polarized photon. A computational approach is employed
of the atom trapped by a finite-sized-box due to a finite basis-set expansion,
which generates a set of transition matrix elements between $E<0$ eigenstates
and $E>0$ pseudostates. We introduce a general computational methodology that
enables the computation of the frequency-dependent dipole transition
polarizability with one real and two different imaginary contributions. These
dipole transition polarizabilities are related to the cross-sections of
one-photon photoionization, Rayleigh, Raman, and Compton scattering. Our
numerical calculations reveal individual Raman scattering cross-sections above
threshold that can rapidly vanish and revive. Furthermore, our numerical
Compton cross-sections do not overtly suffer from the infra-red divergence
problem, and are three orders-of-magnitude higher than previous analytic-based
Compton scattering cross-sections. Our total photon-hydrogen scattering
cross-sections thus resolve the discrepancies between these previous
calculations and those in the N.I.S.T. `FFAST' database.
