  We study a quantum electrodynamics (QED) system made of an two-level atom and
a semi-infinite rectangular waveguide, which behaves as a perfect mirror in one
end. The spatial dependence of the atomic spontaneous emission has been
included in the coupling strength relevant to the eigenmodes of the waveguide.
The role of retardation is studied for the atomic transition frequency far away
from the cutoff frequencies. The atom-mirror distance introduces different
phases and retardation times into the dynamics of the atom interacting
resonantly with the corresponding transverse modes. It is found that the upper
state population decreases from its initial as long as the atom-mirror distance
does not vanish, and is lowered and lowered when more and more transverse modes
are resonant with the atom. The atomic spontaneous emission can be either
suppressed or enhanced by adjusting the atomic location for short retardation
time. There are partial revivals and collapses due to the photon reabsorbed and
re-emitted by the atom for long retardation time.
