{"paper":{"title":"One-dimensional Schr\\\"odinger operators with singular potentials: A Schwartz distributional formulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP","quant-ph"],"primary_cat":"math.SP","authors_text":"Cristina Jorge, Joao Nuno Prata, Nuno Costa Dias","submitted_at":"2016-01-11T02:47:40Z","abstract_excerpt":"Using an extension of the H\\\"ormander product of distributions, we obtain an intrinsic formulation of one-dimensional Schr\\\"odinger operators with singular potentials. This formulation is entirely defined in terms of standard {\\it Schwartz} distributions and does not require (as some previous approaches) the use of more general distributions or generalized functions. We determine, in the new formulation, the action and domain of the Schr\\\"odinger operators with arbitrary singular boundary potentials. We also consider the inverse problem, and obtain a general procedure for constructing the sing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02308","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"}