Improved Lower Bound for Analytic Schrödinger Eigenfunctions in Forbidden Regions

Abstract

The point of this paper is to improve the reverse Agmon estimate discussed in \cite{TW} with assuming that the Schrodinger operator $P(h)=-h^2{\Delta }_g+V-E(h)$, $E(h)\to E$ 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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