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 potentia
l, the total Hamiltonian necessarily has a continuous spectrum in some inte
rvals in between the Landau levels provided that both the amplitude and spa
tial variation of the impurity potential are sufficiently weak. The spatial
decay of the impurity potential is not needed. In particular, this proves
the occurrence of edge states in semi-infinite quantum Hall systems.