Improved Lower Bound for Analytic Schr\"odinger Eigenfunctions in Forbidden Regions
Abstract
The point of this paper is to improve the reverse Agmon estimate discussed in TW with assuming that the Schrodinger operator P(h) = - h2 g + V - E(h), E(h) E as h 0+, is analytic on a compact, real-analytic Riemannian manifold (M,g). In this paper, by considering a Neumann problem with applying Poisson representation and exterior mass estimates on hypersurfaces, we can prove an improved reverse Agmon estimate on a hypersurface.
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