{"paper":{"title":"Recovering the Hamiltonian from spectral data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Cyrille Heriveaux (CMLS-EcolePolytechnique), Thierry Paul (CMLS-EcolePolytechnique)","submitted_at":"2012-02-23T07:56:13Z","abstract_excerpt":"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 Schr\\\"odinger operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5102","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}