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arXiv · 0808.3035

Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators

Michael VanValkenburgh
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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.

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Michael VanValkenburgh. 2008-12-18. Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators. https://arxiv.org/abs/0808.3035

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