Semiclassical Spectral Invariants for Schr\"odinger Operators
Spectral Theory
2009-09-23 v2 Mathematical Physics
math.MP
Abstract
In this article we study the semiclassical spectral measures associated with Schr\"odinger operators on . In particular we compute the first few coefficients of the asymptotic expansions of these measures and, as an application, give an alternative proof of Colin de Verdiere's result on recovering one dimensional potential wells from semiclassical spectral data. We also study the relation of semiclassical spectra measures to Birkhoff normal forms and describe a generalization of the asymptotic expansion above to the Schr\"odinger operator in the presence of a magnetic field.
Cite
@article{arxiv.0905.0919,
title = {Semiclassical Spectral Invariants for Schr\"odinger Operators},
author = {Victor Guillemin and Zuoqin Wang},
journal= {arXiv preprint arXiv:0905.0919},
year = {2009}
}