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Annales Henri Poincaré

, Volume 1, Issue 5, pp 837–883 | Cite as

Exponentially Accurate Semiclassical Dynamics: Propagation, Localization, Ehrenfest Times, Scattering, and More General States

  • G.A. Hagedorn
  • A. Joye

Abstract.

We prove six theorems concerning exponentially accurate semiclassical quantum mechanics. Two of these theorems are known results, but have new proofs. Under appropriate hypotheses, they conclude that the exact and approximate dynamics of an initially localized wave packet agree up to exponentially small errors in \( \hbar \) for finite times and for Ehrenfest times. Two other theorems state that for such times the wave packets are localized near a classical orbit up to exponentially small errors. The fifth theorem deals with infinite times and states an exponentially accurate scattering result. The sixth theorem provides extensions of the other five by allowing more general initial conditions.

Keywords

Quantum Mechanic General State Wave Packet Small Error Finite Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel, 2000

Authors and Affiliations

  • G.A. Hagedorn
    • 1
  • A. Joye
    • 2
  1. 1.Department of Mathematics and Center for Statistical Mechanics and Mathematical Physics, Virginia Polytechnic Institute and State University, Blacksburg, VI 24061-0123, USA, e-mail: hagedorn@math.vt.eduUS
  2. 2.Institut Fourier, Unité Mixte de Recherche CNRS-UJF 5582, Université de Grenoble I, BP 74, F-38402 Saint Martin d'Hères Cedex, France, e-mail: Alain.Joye@ujf-grenoble.frFR

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