{"paper":{"title":"Intertwining semiclassical solutions to a Schr\\\"{o}dinger-Newton system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M\\'onica Clapp, Silvia Cingolani, Simone Secchi","submitted_at":"2011-10-19T09:02:29Z","abstract_excerpt":"We study the problem (-\\epsilon\\mathrm{i}\\nabla+A(x)) ^{2}u+V(x)u=\\epsilon ^{-2}(\\frac{1}{|x|}\\ast|u|^{2}) u, u\\in L^{2}(\\mathbb{R}^{3},\\mathbb{C}),\\text{\\ \\ \\ \\}\\epsilon\\nabla u+\\mathrm{i}Au\\in L^{2}(\\mathbb{R}^{3},\\mathbb{C}^{3}), where $A\\colon\\mathbb{R}^{3}\\rightarrow\\mathbb{R}^{3}$ is an exterior magnetic potential, $V\\colon\\mathbb{R}^{3}\\rightarrow\\mathbb{R}$ is an exterior electric potential, and $\\epsilon$ is a small positive number. If A=0 and $\\epsilon=\\hbar$ is Planck's constant this problem is equivalent to the Schr\\\"odinger-Newton equations proposed by Penrose in \\cite{pe2}\\ to de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4213","kind":"arxiv","version":2},"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"}