  We use the non-equilibrium Green's function formalism along with a
self-consistent Hartree-Fock approximation to numerically study the effects of
a single impurity and interactions between the electrons (with and without
spin) on the conductance of a quantum wire. We study how the conductance varies
with the wire length, the temperature, and the strength of the impurity and
interactions. The dependence of the conductance on the wire length and
temperature is found to be in rough agreement with the results obtained from a
renormalization group analysis based on the Hartree-Fock approximation. For the
spin-1/2 model with a repulsive on-site interaction or the spinless model with
an attractive nearest neighbor interaction, we find that the conductance
increases with increasing wire length or decreasing temperature. This can be
qualitatively explained using the Born approximation in scattering theory. For
a strong impurity, the conductance is significantly different for a repulsive
and an attractive impurity; this is due to the existence of a bound state in
the latter case. In general, the large density deviations at short distances
have an appreciable effect on the conductance which is not captured by the
renormalization group analysis.
