  We present a general method for calculating coherent electronic transport in
quantum wires and tunnel junctions. It is based upon a real space high order
finite difference representation of the single particle Hamiltonian and wave
functions. Landauer's formula is used to express the conductance as a
scattering problem. Dividing space into a scattering region and left and right
ideal electrode regions, this problem is solved by wave function matching (WFM)
in the boundary zones connecting these regions. The method is tested on a model
tunnel junction and applied to sodium atomic wires. In particular, we show that
using a high order finite difference approximation of the kinetic energy
operator leads to a high accuracy at moderate computational costs.
