  Electron transport in a quantum wire with leads is investigated with actual
Coulomb interaction taken into account. The latter includes both the direct
interaction of electrons with each other and their interaction via the image
charges induced in the leads. Exact analytical solution of the problem is found
with the use of the bosonization technique for one-dimensional electrons and
three-dimensional Poisson equation for the electric field. The Coulomb
interaction is shown to change significantly the electron density distribution
along the wire as compared with the Luttinger liquid model with short-range
interactions. In DC and low frequency regimes, the Coulomb interaction causes
the charge density to increase strongly in the vicinity of the contacts with
the leads. The quantum wire impedance shows an oscillating behavior versus the
frequency caused by the resonances of the charge waves. The Coulomb interaction
produces a frequency dependent renormalization of the charge wave velocity.
