  In this work we implement the self-consistent Thomas-Fermi-Poisson approach
to a homogeneous two dimensional electron system (2DES). We compute the
electrostatic potential produced inside a semiconductor structure by a
quantum-point-contact (QPC) placed at the surface of the semiconductor and
biased with appropriate voltages. The model is based on a semi-analytical
solution of the Laplace equation. Starting from the calculated confining
potential, the self-consistent (screened) potential and the electron densities
are calculated for finite temperature and magnetic field. We observe that there
are mainly three characteristic rearrangements of the incompressible "edge"
states, which will determine the current distribution near a QPC.
