Nodal sets for the groundstate of the Schrödinger operator with zero magnetic field in a non simply connected domain.
by
B. Helffer
,
T. Hoffmann-Ostenhof
,
M. P. Owen
| Citations: | 11 - 6 self |
BibTeX
@MISC{Helffer_nodalsets,
author = {B. Helffer and T. Hoffmann-Ostenhof and M. P. Owen},
title = {Nodal sets for the groundstate of the Schrödinger operator with zero magnetic field in a non simply connected domain.},
year = {}
}
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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.
