  We have proposed a semiclassical explanation of the geometric structure of
the spectrum for the two-dimensional Landau Hamiltonian with a two-periodic
electric field without any additional assumptions on the potential. Applying an
iterative averaging procedure we approximately, with any degree of accuracy,
separate variables and describe a given Landau band as the spectrum of a
Harper-like operator. The quantized Reeb graph for such an operator is used to
obtain the following structure of the Landau band: localized states on the band
wings and extended states near the middle of the band. Our approach also shows
that different Landau bands have different geometric structure.
