On the classical limit of the Schrödinger equation

Claude Bardos, François Golse, Peter A. Markowich, Thierry Paul

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

This paper provides an elementary proof of the classical limit of the Schrödinger 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 Schrödinger 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. © 2015, Southwest Missouri State University. All rights reserved.
Original languageEnglish (US)
Pages (from-to)5689-5709
Number of pages21
JournalDiscrete and Continuous Dynamical Systems
Volume35
Issue number12
DOIs
StatePublished - May 2015

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