Mathematical Research Letters

Volume 16, Issue 4, July 2009 pp. 721-734.

Exponential Lower Bounds for Quasimodes of Semiclassical Schr\"{o}dinger Operators

Authors: Michael VanValkenburgh
Author institution: University of California, Los Angeles

Summary: We prove quantitative unique continuation results for the semiclassical Schr-\"{o}dinger 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.

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