2010-11-01, English, Article, Journal or magazine article edition: ON THE HERMAN--KLUK SEMICLASSICAL APPROXIMATION. Robert, Didier

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Physical Description
  • Magazine/​Journal article
Published
  • World Scientific Publishing Co. Pte Ltd., 2010 Nov
Language
  • English

Edition details

Title
  • ON THE HERMAN--KLUK SEMICLASSICAL APPROXIMATION.
Appears In
  • Reviews in Mathematical Physics, v.22, no.10, 2010 Nov, p.1123 (ISSN: 0129-055X)
Author
  • Robert, Didier
Published
  • World Scientific Publishing Co. Pte Ltd., 2010 Nov
Physical Description
  • Magazine/​Journal article
Subjects
Target Audience
  • Academic
Summary
  • To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http:/​/​dx.doi.org/​10.1142/​S0129055X1000417X Byline: DIDIER ROBERT For a subquadratic symbol H on a.sup.d x a.sup.d = T*(a.sup.d), the quantum propagator of the time dependent Schrodinger equation $i\hbar\frac{\partial\psi}{\partial t} = \hat H\psi$ is a Semiclassical Fourier-Integral Operator when A[currency] = H(x, aD.sub.x) (a-Weyl quantization of H). Its Schwartz kernel is described by a quadratic phase and an amplitude. At every time t, when a is small, it is "essentially supported" in a neighborhood of the graph of the classical flow generated by H, with a full uniform asymptotic expansion in a for the amplitude. In this paper, our goal is to revisit this well-known and fundamental result with emphasis on the flexibility for the choice of a quadratic complex phase function and on global L.sup.2 estimates when a is small and time t is large. One of the simplest choice of the phase is known in chemical physics as Herman--Kluk formula. Moreover, we prove that the semiclassical expansion for the propagator is valid for $|t|\ll \frac{1}{4\delta}|{{\rm log}}\, \hbar|$ where I[acute accent] > 0 is a stability parameter for the classical system.
Terms of Use
  • COPYRIGHT 2010 World Scientific Publishing Co. Pte Ltd.
Language
  • English
Database
  • Gale Academic OneFile
Identifier
  • 462419826
  • 10.1142/​S0129055X1000417X

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