Two regions of a two-dimensional electron gas of carrier density n=2.1\\\\times 1010 cm2\ are connected by a thin, ballistic channel. The confining potential in the channel is ?(?)=??2?2/2\ where ?=0.10??\ is the electron effective mass, ??\ is the free electron mass, ?=2.8\\\\times 1011\ rads1\ and ?\ is the distance from the centre of the channel. The electrons are free to move in the ?\ -direction in the channel. The background potential in the electron gases is ?=0\ , and there are two degenerate spin components. Determine the conductance of the device at low temperature. All answers are in units of ?2/\ .