The total number N of propagating modes at energy E is determined by the maximum flux max contained in an area bounded by the channel walls and a circle of radius (2mE)1/2/eB, according to N = Int[e max/h + γ/2π]. Note that a maximal enclosed flux is obtained by centering the circle on the channel axis. Some simple geometry then leads to the result80 (2.62), which is plotted together with that for a parabolic confinement in Fig. 31. Equation (2.62) has a discontinuity at magnetic fields for which the cyclotron diameter equals the channel width, due to the jump in the phase shift γ as one goes from a cyclotron orbit to a traversing trajectory. This jump is an artifact of the present semiclassical approximation in which the extension of the wave function beyond the classical orbit is ignored. Since the discontinuity in N is at most ±1, it is unimportant in many applications. More accurate formulas for the phase shift γ, which smooth out the discontinuity, have been derived in Ref.270. If necessary, one can also use more complicated but exact solutions of the Schr¨odinger equation, which are known.267