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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
DOI: https://doi.org/10.1090/S0002-9939-2011-11517-X
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.

References [Enhancements On Off] (What's this?)

  • [AHS] J. Avron, I. Herbst, B. Simon, Schrödinger Operators with Magnetic Fields, I. General Interactions, Duke Math. J. $ \mathbf {45}$, 847-883 (1978). MR 518109 (80k:35054)
  • [B] H. Baum, Spin-Strukturen und Dirac-Operatoren über Pseudoriemannschen Mannigfaltigkeiten, Teubner Verlagsgesellschaft, Leipzig, 1981. MR 701244 (84m:58160)
  • [D] A. Dufresnoy, Un Example de Champ Magnétique dans $ \mathbf {R}^{\nu }$, Duke Math. J. $ \mathbf {50}$, 729-734 (1983). MR 714827 (84k:78005)
  • [HM] B. Helffer, A. Mohamed, Caractérisation du Spectre Essentiel de l'Opérateur de Schrödinger avec un Champ Magnétique, Ann. Inst. Fourier $ \mathbf {38}$, 95-112 (1988). MR 949012 (90d:35215)
  • [I] A. Iwatsuka, Magnetic Schrödinger Operators with Compact Resolvent, J. Math. Kyoto Univ. $ \mathbf {26}$, 357-374 (1986). MR 857223 (87j:35287)
  • [KS] V. Kondratiev, M. Shubin, Discreteness of Spectrum for the Magnetic Schrödinger Operators, Commun. Partial Diff. Eqns. $ \mathbf {27}$, 477-525 (2002). MR 1900553 (2003f:35058)
  • [LM] B. Lawson, M-L. Michelsohn, Spin Geometry, Princeton Univ. Press, Princeton, NJ, 1989. MR 1031992 (91g:53001)

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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-2011-11517-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.

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