  Using the recursive Green's function technique, we study the coherent
electron conductance of a quantum point contact in the presence of a scanning
probe microscope tip. Images of the coherent fringe inside a quantum point
contact for different widths are obtained. It is found that the conductance of
a specific channel is reduced while other channels are not affected as long as
the tip is located at the positions correspending to that channel. Moreover,
the coherent fringe is smoothed out by increasing the temperature or the
voltage across the device. Our results are consistent with the experiments
reported by Topinka et al.[Science 289, 2323 (2000)].
