Advances in Mathematical Physics
Volume 2009 (2009), Article ID 873704, 15 pages
doi:10.1155/2009/873704
Research Article

Eigenvalue Asymptotics of the Even-Dimensional Exterior Landau-Neumann Hamiltonian

Mikael Persson

Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University, 412 96 Göteborg, Sweden

Received 27 June 2008; Accepted 22 October 2008

Academic Editor: Pavel Exner

Copyright © 2009 Mikael Persson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the Schrödinger operator with a constant magnetic field in the exterior of a compact domain in ℝ2d, d≥1. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We give asymptotic formulas for the rate of accumulation of eigenvalues in these clusters. When the compact is a Reinhardt domain we are able to show a more precise asymptotic formula.