  The classical drift motion of electrons in crossed electric and magnetic
fields provides an interesting example of a system with an on average constant
velocity -- despite the presence of an electric field. This drift-velocity
depends solely on the ratio of the electric and magnetic fields and not on the
initial momentum of the electron. The present work describes the
quantum-mechanical version of this drift-motion, which differs drastically from
the classical result: The drift becomes dependent on the energy and a
quantization of the transport occurs. The results bear implications for the
theory of the quantum Hall effect: Current theories neglect the electric
Hall-field (which is perpendicular to a magnetic field) and thus do not include
the quantization due to the crossed-field geometry. I will discuss why it is
not possible to eliminate the electric field and how one can explain the
quantization in crossed fields in a semiclassical picture. These results make
it possible to construct an alternative theory of the quantum Hall effect.
