Mathematical Research Letters

Volume 16 (2009)

Number 4

Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators

Pages: 721 – 734



Michael VanValkenburgh (University of California at Los Angeles)


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.

Published 1 January 2009