Nodal Sets for Groundstates of Schrödinger Operators with Zero Magnetic Field in Non Simply Connected Domains
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.
KeywordsMagnetic Field Electric Potential Vector Potential Magnetic Vector Connected Domain
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