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On the Eigenvalues of a Perturbed Harmonic Oscillator

  • Anne Boutet de Monvel-Berthier
Chapter
Part of the Mathematical Physics Studies book series (MPST, volume 12)

Abstract

We study Schrödinger operators on Rn of the form
$$H = {H_v} = - \Delta + q(x) + V(x) $$
where q(x) is a positive definite quadratic form and V(x) a potential which may be considered as a perturbation. We show that the discrete spectrum of H has similar properties as that of the unperturbed H0 = -∆+q. In particular the singular points of the distribution on R: t → Tr eitH are the lengths of the periodic orbits of the hamiltonian flow associated to H0.This work was done in collaboration with G.Lebeau and L.Boutet de Monvel.

Keywords

Pseudodifferential Operator Trace Formula Fourier Integral Operator Symbolic Calculus Microlocal Analysis 
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 Science+Business Media Dordrecht 1991

Authors and Affiliations

  • Anne Boutet de Monvel-Berthier
    • 1
  1. 1.Laboratoire de Physique Mathématique et GéométrieUniversité Paris VIIParis Cedex 05France

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