  We study the space-time structure of the scattered field induced by the
scattering of a narrow single-photon Gaussian pulse on a qubit embedded in 1D
open waveguide. For a weak excitation power we obtain explicit analytical
expressions for space and time dependence of reflected and transmitted fields
which are, in general, are different from plain travelling waves. The scattered
field consists of two parts: a damping part which represent a spontaneous decay
of the excited qubit and a coherent, lossless part. We show that for large
distance $x$ from qubit and at times $t$ long after the scattering event our
theory provides the result which is well known from the stationary photon
transport. However, the approach to the stationary limit is very slow. The
scattered field decreases as the inverse powers of $x$ and $t$ as both the
distance from the qubit and the time after the interaction increase.
