  A quantum point contact (QPC) patterned on a two-dimensional electron gas is
investigated with a scanning gate setup operated at a temperature of 300 mK.
The conductance of the point contact is recorded while the local potential is
modified by scanning the tip. Single electron charging of impurities induced by
the local potential is observed as a stepwise conductance change of the
constriction. By selectively changing the state of some of these impurities, it
is possible to observe changes in transmission resonances of the QPC. The
location of such impurities is determined, and their density is estimated to be
below 50 per \mu m^2, corresponding to less than 1 % of the doping
concentration.
