{"paper":{"title":"Dispersive estimate for the 1D Schr\\\"odinger equation with a steplike potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Piero D'Ancona, Sigmund Selberg","submitted_at":"2010-10-17T18:08:30Z","abstract_excerpt":"We prove a sharp dispersive estimate $$ |P_{ac}u(t,x)|\\le C|t|^{-1/2}\\|u(0)\\|_{L^1(R)} $$ for the one dimensional Schr\\\"odinger equation $$ iu_{t}-u_{xx}+V(x)u+V_0 u=0, $$ where $(1+x^2)V\\in L^1(R)$ and $V_0$ is a step function, real valued and consant on the positive and negative real axes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3433","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"}