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 [TW20] with assuming that the Schrodinger operator Pis 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.