## Recovering the Hamiltonian from spectral data    [PDF]

Cyrille Heriveaux, Thierry Paul
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
$\gamma$.
View original: http://arxiv.org/abs/1202.5102