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hal-00250568, version 1

A semi-classical inverse problem I: Taylor expansions.

Yves Colin De Verdière () 1, Victor Guillemin 2

Abstract: In dimension 1, we show that the Taylor expansion of a potential near a generic non degenerate critical point can be recovered from the knowledge of the semi-classical spectrum of the associated Schrödinger operator near the corresponding critical value.

  • 1:  Institut Fourier (IF)
  • CNRS : UMR5582 – Université Joseph Fourier - Grenoble I
  • 2:  Math. Dep.
  • MIT
  • Domain : Mathematics/Mathematical Physics
    Physics/Mathematical Physics
    Mathematics/Analysis of PDEs
    Mathematics/Spectral Theory
  • Keywords : Schrödinger operator – semi-classics – inverse spectral problem – trace formulae – Birkhoff normal form
  • Internal note : IF_PREPUB
  • Comment : 15 pages
 
  • hal-00250568, version 1
  • http://hal.archives-ouvertes.fr/hal-00250568
  • oai:hal.archives-ouvertes.fr:hal-00250568
  • From: Yves Colin de Verdière <>
  • Submitted on: Tuesday, 12 February 2008 09:56:51
  • Updated on: Friday, 13 February 2009 15:12:58