Mathematical Research Letters
Volume 20 (2013)
Pointwise bounds on quasimodes of semiclassical Schrödinger operators in dimension two
Pages: 401 – 408
We prove sharp pointwise bounds on quasimodes of semiclassical Schrödinger operators with arbitrary smooth real potentials in dimension two. This end-point estimate was left open in the general study of semiclassical $L^p$ bounds conducted by Koch et al. . However, we show that the results of  imply the two-dimensional end-point estimate by scaling and localization.