On the classical limit of the Schrödinger equation
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 equat...
Published in: | Discrete and Continuous Dynamical Systems |
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Main Authors: | , , , |
Other Authors: | , , , |
Format: | Article in Journal/Newspaper |
Language: | unknown |
Published: |
American Institute of Mathematical Sciences (AIMS)
2015
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Subjects: | |
Online Access: | http://hdl.handle.net/10754/594257 https://doi.org/10.3934/dcds.2015.35.5689 |
Summary: | 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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