Recovering the Hamiltonian from spectral data
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- by C. Hériveaux and T. Paul PDF
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Abstract:
We show that the contributions to the Gutzwiller formula with observables associated to the iterates of a given elliptic non-degenerate periodic trajectory $\gamma$ and to certain families of observables localized near $\gamma$ determine the quantum Hamiltonian in a formal neighborhood of the trajectory $\gamma$, that is, the full Taylor expansion of its total symbol near $\gamma$. We also treat the “bottom of a well” case both for general and Schrödinger operators, and give some analog classical results.References
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Additional Information
- C. Hériveaux
- Affiliation: CMLS École polytechnique, 91 128 Palaiseau cedex, France
- Email: cyrille.heriveaux@math.polytechnique.fr
- T. Paul
- Affiliation: CNRS and CMLS École polytechnique, 91 128 Palaiseau cedex, France
- Email: thierry.paul@polytechnique.edu
- Received by editor(s): November 14, 2013
- Received by editor(s) in revised form: September 15, 2014
- Published electronically: January 27, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 7239-7279
- MSC (2010): Primary 35-XX, 37-XX, 41-XX, 58-XX, 81-XX
- DOI: https://doi.org/10.1090/tran/6566
- MathSciNet review: 3471090