TY - JOUR
T1 - On the classical limit of the Schrödinger equation
AU - Bardos, Claude
AU - Golse, François
AU - Markowich, Peter A.
AU - Paul, Thierry
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2015/5
Y1 - 2015/5
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/594257
UR - http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11197
UR - http://www.scopus.com/inward/record.url?scp=84930257503&partnerID=8YFLogxK
U2 - 10.3934/dcds.2015.35.5689
DO - 10.3934/dcds.2015.35.5689
M3 - Article
SN - 1078-0947
VL - 35
SP - 5689
EP - 5709
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 12
ER -