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Nodal Sets for Groundstates of Schrödinger Operators with Zero Magnetic Field in Non Simply Connected Domains

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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.

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Received: 23 July 1998 / Accepted: 17 November 1998

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Helffer, B., Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T. et al. Nodal Sets for Groundstates of Schrödinger Operators with Zero Magnetic Field in Non Simply Connected Domains. Comm Math Phys 202, 629–649 (1999). https://doi.org/10.1007/s002200050599

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  • DOI: https://doi.org/10.1007/s002200050599

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