Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators

Abstract

We prove quantitative unique continuation results for the semiclassical Schrodinger operator on smooth, compact domains. These take the form of exponentially decreasing (in h) local L^{2} lower bounds for exponentially precise quasimodes. We also show that these lower bounds are sharp in h, and that, moreover, the hypothesized quasimode accuracy is also sharp.

14 pages, no figures; cosmetic changes. Final version, to appear in Mathematical Research Letters