{"paper":{"title":"Matrix representation of the time operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Carl M. Bender, M. Gianfreda","submitted_at":"2012-01-18T16:25:24Z","abstract_excerpt":"In quantum mechanics the time operator $\\Theta$ satisfies the commutation relation $[\\Theta,H]=i$, and thus it may be thought of as being canonically conjugate to the Hamiltonian $H$. The time operator associated with a given Hamiltonian $H$ is not unique because one can replace $\\Theta$ by $\\Theta+ \\Theta_{\\rm hom}$, where $\\Theta_{\\rm hom}$ satisfies the homogeneous condition $[\\Theta_{\\rm hom},H]=0$. To study this nonuniqueness the matrix elements of $\\Theta$ for the harmonic-oscillator Hamiltonian are calculated in the eigenstate basis. This calculation requires the summation of divergent "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3838","kind":"arxiv","version":1},"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"}