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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a class of magnetic Schrödinger operators with discrete spectrum


Author: N. Anghel
Journal: Proc. Amer. Math. Soc. 140 (2012), 1613-1616
MSC (2010): Primary 35J10; Secondary 35P05, 47F05, 81V10
Published electronically: December 23, 2011
MathSciNet review: 2869145
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Abstract: We introduce a class of magnetic Schrödinger operators in $ \mathbf {R}^n$ which exhibit pure point spectrum in a fashion that is actually easy to check. This class is an adequate generalization of the more familiar two-dimensional setting, and the proof we give for its spectral discreteness is novel, based on the use of Euclidean Dirac operators coupled to vector potentials.


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Additional Information

N. Anghel
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: anghel@unt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11517-X
PII: S 0002-9939(2011)11517-X
Keywords: Schrödinger operator, magnetic field, discrete spectrum, Dirac operator
Received by editor(s): January 5, 2011
Published electronically: December 23, 2011
Communicated by: Varghese Mathai
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.