Ballistic electronic conductance of an orifice

We rigorously treat the quantum-mechanical ballistic propagation of a two-dimensional noninteracting-electron gas in a region where the electrons are free except for their interaction with the boundaries of the region. We compute the conductance of an orifice as a function of its width and length. The basic global structure of the conductance when the length is large reveals nearly quantized jumps of 2$e^2$/h as the width varies. A closer inspection shows oscillatory behavior between the plateaus. Both quantization and oscillations are explained in terms of a simple description based on barrier penetration, longitudinal wave resonances, and impedance matching.