  The theme of this work is that the theory of charged particles in a uniform
magnetic field can be generalized to a large class of operators if one uses an
extended a class of Weyl operators which we call "Landau--Weyl
pseudodifferential operators". The link between standard Weyl calculus and
Landau--Weyl calculus is made explicit by the use of an infinite family of
intertwining "windowed wavepacket transforms"; this makes possible the use of
the theory of modulation spaces to study various regularity properties. Our
techniques allow us not only to recover easily the eigenvalues and
eigenfunctions of the Hamiltonian operator of a charged particle in a uniform
magnetic field, but also to prove global hypoellipticity results and to study
the regularity of the solutions to Schroedinger equations.
