I will discuss a trace formula for the eigenvalue clusters
of the Landau
Hamiltonian (i.e. the 2D Schroedinger operator with a
constant  magnetic
field), perturbed by an electric potential which decays at
infinity. The
spectrum of this Hamiltonian consists of clusters of
eigenvalues which
accumulate to the Landau levels. The asymptotic density of
eigenvalues in these clusters is studied when the cluster
number tends to
infinity. This asymptotic density is described explicitly
in terms of the
Radon transform of the perturbation potential. The main
tools applied in
the proofs of the results, are pseudodifferential
operators with contravariant symbols.
This is a joint work with A. Pushnitski (King's College,
London, UK) and
Carlos Villegas-Blas (UNAM, Cuernavaca, Mexico).
Partially supported by the Chilean Science Foundation
Fondecyt under Grant
1090467.