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KAM for the Quantum Harmonic Oscillator

  • Benoît GrébertEmail author
  • Laurent Thomann
Article

Abstract

In this paper we prove an abstract KAM theorem for infinite dimensional Hamiltonians systems. This result extends previous works of S.B. Kuksin and J. Pöschel and uses recent techniques of H. Eliasson and S.B. Kuksin. As an application we show that some 1D nonlinear Schrödinger equations with harmonic potential admits many quasi-periodic solutions. In a second application we prove the reducibility of the 1D Schrödinger equations with the harmonic potential and a quasi periodic in time potential.

Keywords

Normal Form Harmonic Oscillator Harmonic Potential Sobolev Embedding Hermite Function 
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

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques J. LerayUniversité de Nantes, UMR CNRS 6629Nantes Cedex 03France

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