  We calculate the electronic width of quantum wires as a function of their
lithographic width in analogy to experiments performed on nanostructures
defined by local oxidation of Ga[Al]As heterostructures. Two--dimensional
simulations of two parallel oxide lines on top of a Ga[Al]As heterostructure
defining a quantum wire are carried out in the framework of Density Functional
Theory in the Local Density Approximation and are found to be in agreement with
measurements. Quantitative assessment of the influence of various experimental
uncertainties is given. The most influential parameter turns out to be the
oxide line depth, followed by its exact shape and the effect of background
doping (in decreasing order).
