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ON THE CLASSICAL LIMIT OF THE SCHRODINGER EQUATION
Journal article   Open access  Peer reviewed

ON THE CLASSICAL LIMIT OF THE SCHRODINGER EQUATION

Claude Bardos, Francois Golse, Peter Markowich and Thierry Paul
Discrete and continuous dynamical systems. Series A, Vol.35(12), pp.5689-5709
01/12/2015

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
This paper provides an elementary proof of the classical limit of the Schrodinger 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 Schriidinger 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.
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https://doi.org/10.3934/dcds.2015.35.5689View
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