The subject of the talk is the spectrum of the Landau Hamiltonian (i.e. the two-dimensional Schrodinger operator with a constant homogeneous magnetic field)perturbed by an electric potential which decays sufficiently fast at infinity. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. It turns out that the the density of eigenvalues in the N'th cluster for large N can be described by means of a simple semiclassical formula. The formula involves the Radon transform of the potential. The formula has been inspired by the classical result of A.Weinstein on the eigenvalue clusters for a Laplacian plus a potential on a sphere. The talk is based on a recent joint work with Georgi Raikov and Carlos Villegas-Blas.
Seminar on Analysis at University of Tsukuba