{"paper":{"title":"1D Schr\\\"{o}dinger operators with short range interactions: two-scale regularization of distributional potentials","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.SP","authors_text":"Yuriy Golovaty","submitted_at":"2012-02-21T17:38:04Z","abstract_excerpt":"For real bounded functions \\Phi and \\Psi of compact support, we prove the norm resolvent convergence, as \\epsilon and \\nu tend to 0, of a family of one-dimensional Schroedinger operators on the line of the form S_{\\epsilon, \\nu}= -D^2+\\alpha\\epsilon^{-2}\\Phi(\\epsilon^{-1}x)+\\beta\\nu^{-1}\\Psi(\\nu^{-1}x), provided the ratio \\nu/\\epsilon has a finite or infinity limit. The limit operator S_0 depends on the shape of \\Phi and \\Psi as well as on the limit of ratio \\nu/\\epsilon. If the potential \\alpha\\Phi possesses a zero-energy resonance, then S_0 describes a non trivial point interaction at the or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4711","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"}