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Nodal Sets for Groundstates of Schrödinger Operators with Zero Magnetic Field in Non Simply Connected Domains |
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| Authors: | B Helffer M Hoffmann-Ostenhof T Hoffmann-Ostenhof M P Owen |
| Institution: | Département de Mathématiques, Batiment 425, Université Paris-Sud, F-91405 Orsay Cedex, France.?E-mail: bernard.helffer@math.u-psud.fr, FR Institut für Mathematik, Universit?t Wien, Strudthofgasse 4, A-1090 Wien, Austria.?E-mail: mho@nelly.mat.univie.ac.at, AT Institut für Theoretische Chemie, Universit?t Wien, W?hringerstrasse 17, A-1090 Wien, Austria.?E-mail: hoho@itc.univie.ac.at, AT International Erwin Schr?dinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Wien,?Austria. E-mail: mowen@wiener.fam.tuwien.ac.at, AT |
| Abstract: | We investigate nodal sets of magnetic Schr?dinger 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. Received: 23 July 1998 / Accepted: 17 November 1998 |
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