Eigenvalue Clusters of the Landau Hamiltonian in the Exterior of a Compact Domain

We consider the Schrödinger operator with a constant magnetic field in the exterior of a compact domain on the plane. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We discuss the rate of accumulation of eigenvalues in a fixed cluster.

2000 Mathematics Subject Classification: Primary 35P20; Secondary 35Q40.

Keywords and Phrases: Schrödinger operator, magnetic field, spectral asymptotics, exterior problem

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