Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators

We prove quantitative unique continuation results for the semiclassical Schr-ödinger 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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Published 1 January 2009