Nodal sets for the groundstate of the Schroedinger operator with zero magnetic field in a non simply connected domain

Details Nodal sets for the groundstate of the Schroedinger operator with zero magnetic field in a non simply connected domain Nodal sets for the groundstate of the Schroedinger operator with zero magnetic field in a non simply connected domain

1998-07-13

arxiv.org/abs/math/9807064v1

Mathematics

Spectral Theory

30 pages, 8 figures

Scientific paper

10.1007/s002200050599

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 charactisation 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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