{"paper":{"title":"Solution of the time dependent Schr\\\"odinger equation leading to Fowler-Nordheim field emission","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ian Jauslin, Joel L. Lebowitz, Ovidiu Costin, Rodica D. Costin","submitted_at":"2018-08-02T17:42:42Z","abstract_excerpt":"We solve the time-dependent Schr\\\"odinger equation describing the emission of electrons from a metal surface by an external electric field $E$, turned on at $t=0$. Starting with a wave function $\\psi(x,0)$, representing a generalized eigenfunction when $E=0$, we find $\\psi(x,t)$ and show that it approaches, as $t\\to\\infty$, the Fowler-Nordheim tunneling wavefunction $\\psi_E$. The deviation of $\\psi$ from $\\psi_E$ decays asymptotically as a power law $t^{-\\frac32}$. The time scales involved for typical metals and fields of several V/nm are of the order of femtoseconds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00936","kind":"arxiv","version":3},"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"}