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Journal Articles Discrete and Continuous Dynamical Systems - Series A Year : 2015

On the Classical Limit of the Schrödinger Equation

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Claude Bardos
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  • PersonId : 890454
François Golse
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  • PersonId : 838357
Peter Markowich
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  • PersonId : 848885
Thierry Paul
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  • PersonId : 883128

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.
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Dates and versions

hal-01074071 , version 1 (12-10-2014)

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Claude Bardos, François Golse, Peter Markowich, Thierry Paul. On the Classical Limit of the Schrödinger Equation. Discrete and Continuous Dynamical Systems - Series A, 2015, 35 (12), pp.5689-5709. ⟨10.3934/dcds.2015.35.5689⟩. ⟨hal-01074071⟩
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