  We consider an electron in two dimensions submitted to a magnetic field and
to the potential of impurities. We show that when the electron is confined to a
half-space by a planar wall described by a smooth increasing potential, the
total Hamiltonian necessarily has a continuous spectrum in some intervals
in-between the Landau levels provided that both the amplitude and spatial
variation of the impurity potential are sufficiently weak. The spatial decay of
the impurity potential is not needed. In particular this proves the occurence
of edge states in semi-infinite quantum Hall systems.
