  Using the procedures in \cite{Bu} and \cite{GMS} and the magnetic
pseudodifferential calculus we have developped in \cite{MP1,MPR1,IMP1,IMP2} we
construct an effective Hamitonian that describes the spectrum in any compact
subset of the real axis for a large class of periodic pseudodifferential
Hamiltonians in a bounded smooth magnetic field, in a completely gauge
covariant setting, without any restrictions on the vector potential and without
any adiabaticity hypothesis.
