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arXiv · 2108.08519

Improved Lower Bound for Analytic Schrödinger Eigenfunctions in Forbidden Regions

Xianchao Wu
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Abstract

The point of this paper is to improve the reverse Agmon estimate discussed in \cite{TW} with assuming that the Schrodinger operator $P(h) = - h^2 Δ_g + V - E(h)$, $E(h)\to E$ as $h\to 0^+$, 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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Xianchao Wu. 2021-08-19. Improved Lower Bound for Analytic Schrödinger Eigenfunctions in Forbidden Regions. https://arxiv.org/abs/2108.08519

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