Recovering the Hamiltonian from spectral data
Abstract
We show that the contributions to the Gutzwiller formula with observable associated to the iterates of a given elliptic nondegenerate 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2012
 DOI:
 10.48550/arXiv.1202.5102
 arXiv:
 arXiv:1202.5102
 Bibcode:
 2012arXiv1202.5102H
 Keywords:

 Mathematical Physics;
 Quantum Physics