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arXiv · 1410.4030

On the Classical Limit of the Schr\"{o}dinger Equation

Claude Bardos·François Golse·Peter Markowich·Thierry Paul
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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.

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Claude Bardos, François Golse, Peter Markowich, Thierry Paul. 2014-10-15. On the Classical Limit of the Schr\"{o}dinger Equation. https://doi.org/10.3934/dcds.2015.35.5689

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