Conductance quantization in a general confining potential

We show that conductance quantization can be obtained in a quite general smooth confining potential, provided that it creates a narrow bottleneck region. Precise criteria for the necessary smoothness are derived. It is shown that even rapid fluctuations in the confining potential, on length scales less than the Fermi wavelength, affect the conductance only slightly as long as they are far from the narrow region. We show that constrictions that widen sharply are less sensitive to imperfections in the confining potential.