Abstract
This note concerns the nodal sets of eigenfunctions of semiclassical Schrödinger operators acting on compact, smooth, Riemannian manifolds, with no boundary. In the case of real analytic surfaces, we obtain sharp upper bounds for the number of intersections of the zero sets of Schrödinger eigenfunctions with a fixed curve that lies inside the classically forbidden region.
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Communicated by Jens Marklof.
Yaiza Canzani was partially supported by an NSERC Postdoctoral Fellowship and by NSF Grant DMS-1128155. John A. Toth was partially supported by NSERC Grant OGP0170280.
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Canzani, Y., Toth, J.A. Nodal Sets of Schrödinger Eigenfunctions in Forbidden Regions. Ann. Henri Poincaré 17, 3063–3087 (2016). https://doi.org/10.1007/s00023-016-0488-3
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DOI: https://doi.org/10.1007/s00023-016-0488-3