98-503 Helffer B., Hoffmann-Ostenhof M., Hoffmann-Ostenhof T., Owen M. P.

Nodal sets for the groundstate of the Schroedinger operator with zero magnetic field in a non simply connected domain. (129K, LaTeX 2e) Jul 13, 98

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Abstract. We investigate nodal sets of magnetic Schroedinger operators with zero magnetic field, acting on a non simply connected domain in $\r^2$. 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 $1/2$.

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