{"paper":{"title":"Atoms confined by very thin layers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Matej Tusek","submitted_at":"2012-05-10T13:42:00Z","abstract_excerpt":"The Hamiltonian of an atom with $N$ electrons and a fixed nucleus of infinite mass between two parallel planes is considered in the limit when the distance $a$ between the planes tends to zero. We show that this Hamiltonian converges in the norm resolvent sense to a Schr\\\"{o}dinger operator acting effectively in $L^{2}(\\mathbb{R}^{2N})$ whose potential part depends on $a$. Moreover, we prove that after an appropriate regularization this Schr\\\"{o}dinger operator tends, again in the norm resolvent sense, to the Hamiltonian of a two-dimensional atom (with the three-dimensional Coulomb potential-o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2260","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"}