The Fate of the Landau Levels under Perturbations of Constant Sign
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Date
2009
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Publisher
OXFORD UNIV PRESS
Abstract
We show that the Landau levels cease to be eigenvalues if we perturb the 2D Schrodinger operator with a constant magnetic field, by bounded electric potentials of fixed sign. We also show that, if the perturbation is not of fixed sign, then any Landau level may be an eigenvalue of the perturbed problem.
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Keywords
SCHRODINGER-OPERATORS, EIGENVALUE ASYMPTOTICS, SPECTRAL ASYMPTOTICS, MAGNETIC-FIELDS