We present new theoretical results describing the observed spectra and pulse profiles for radiation emitted in the pencil and fan beam components from a dipole-shaped accretion column in an X-ray pulsar. The spectral calculations are based on the model of West, Wolfram, & Becker (2017), who for the first time solved a fully self-consistent photon transport equation coupled with a rigorous set of dynamical equations and boundary conditions that includes the effects of both radiation pressure and gas pressure in a dipole magnetic field geometry. The simulation of the observed spectra and pulse profiles is accomplished by integrating the height-dependent spectrum emerging from both the walls and top of the accretion column, coupled with the effects of general relativistic light-bending and redshifting. The resulting self-consistent radiation-hydrodynamical model provides the most robust theoretical platform currently available for the interpretation of phase-dependent spectra and pulse profiles. We compare the model results with the observed spectra and pulse profiles for the high-luminosity source Her X-1.