On the Classical Limit of the Schr\"{o}dinger Equation
Analysis of PDEs
2015-06-03 v1 Mathematical Physics
math.MP
Abstract
This paper provides an elementary proof of the classical limit of the Schr\"{o}dinger equation with WKB type initial data and over arbitrary long finite time intervals. We use only the stationary phase method and the Laptev-Sigal simple and elegant construction of a parametrix for Schr\"{o}dinger type equations [A. Laptev, I. Sigal, Review of Math. Phys. 12 (2000), 749-766]. We also explain in detail how the phase shifts across caustics obtained when using the Laptev-Sigal parametrix are related to the Maslov index.
Keywords
Cite
@article{arxiv.1410.4030,
title = {On the Classical Limit of the Schr\"{o}dinger Equation},
author = {Claude Bardos and François Golse and Peter Markowich and Thierry Paul},
journal= {arXiv preprint arXiv:1410.4030},
year = {2015}
}
Comments
21 pages