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Communications in Mathematical Physics

, Volume 202, Issue 3, pp 629–649 | Cite as

Nodal Sets for Groundstates of Schrödinger Operators with Zero Magnetic Field in Non Simply Connected Domains

  • B. Helffer
  • M. Hoffmann-Ostenhof
  • T. Hoffmann-Ostenhof
  • M. P. Owen

Abstract:

We investigate nodal sets of magnetic Schrödinger operators with zero magnetic field, acting on a non simply connected domain in ℝ2. For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a characterisation of the nodal set, and use this to obtain bounds on the multiplicity of the groundstate. For the case of one hole and a fixed electric potential, we show that the first eigenvalue takes its highest value for circulation 1/2.

Keywords

Magnetic Field Electric Potential Vector Potential Magnetic Vector Connected Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • B. Helffer
    • 1
  • M. Hoffmann-Ostenhof
    • 2
  • T. Hoffmann-Ostenhof
    • 3
  • M. P. Owen
    • 4
  1. 1.Département de Mathématiques, Bâtiment 425, Université Paris-Sud, F-91405 Orsay Cedex, France.¶E-mail: bernard.helffer@math.u-psud.frFR
  2. 2.Institut für Mathematik, Universität Wien, Strudthofgasse 4, A-1090 Wien, Austria.¶E-mail: mho@nelly.mat.univie.ac.atAT
  3. 3.Institut für Theoretische Chemie, Universität Wien, Währingerstrasse 17, A-1090 Wien, Austria.¶E-mail: hoho@itc.univie.ac.atAT
  4. 4.International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Wien,¶Austria. E-mail: mowen@wiener.fam.tuwien.ac.atAT

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