  We consider propagation of a two-level atom coupled to one electro-magnetic
mode of a high-Q cavity. The atomic center-of-mass motion is treated quantum
mechanically and we use a standing wave shape for the mode. The periodicity of
the Hamiltonian leads to a spectrum consisting of bands and gaps, which is
studied from a Floquet point of view. Based on the band theory we introduce a
set of effective mass parameters that approximately describe the effect of the
cavity on the atomic motion, with the emphasis on one associated with the group
velocity and on another one that coincides with the conventional effective
mass. Propagation of initially Gaussian wave packets is also studied using
numerical simulations and the mass parameters extracted thereof are compared
with those predicted by the Floquet theory. Scattering and transmission of the
wave packet against the cavity are further analyzed, and the constraints for
the effective mass approach to be valid are discussed in detail.
