{"paper":{"title":"Gamow Vectors in a Periodically Perturbed Quantum System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Min Huang","submitted_at":"2009-04-26T17:30:42Z","abstract_excerpt":"We analyze the behavior of the wave function $\\psi(x,t)$ for one dimensional time-dependent Hamiltonian $H=-\\partial_x^2\\pm2\\delta(x)(1+2r\\cos\\omega t)$ where $\\psi(x,0)$ is compactly supported. We show that $\\psi(x,t)$ has a Borel summable expansion containing finitely many terms of the form $\\sum_{n=-\\infty}^{\\infty} e^{i^{3/2}\\sqrt{-\\lambda_{k}+n\\omegai}|x|} A_{k,n} e^{-\\lambda_{k}t+n\\omega it}$, where $\\lambda_k$ represents the associated resonance. This expression defines Gamow vectors and resonances in a rigorous and physically relevant way for all frequencies and amplitudes in a time-de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4040","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"}