{"paper":{"title":"Semiclassical Szeg\\\"o limit of eigenvalue clusters for the hydrogen atom Zeeman Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Carlos Villegas-Blas, Misael Avendano-Camacho, Peter D. Hislop","submitted_at":"2017-01-24T13:38:27Z","abstract_excerpt":"We prove a limiting eigenvalue distribution theorem (LEDT) for suitably scaled eigenvalue clusters around the discrete negative eigenvalues of the hydrogen atom Hamiltonian formed by the perturbation by a weak constant magnetic field. We study the hydrogen atom Zeeman Hamiltonian $H_V(h,B) = (1/2)( - i h {\\mathbf \\nabla} - {\\mathbf A}(h))^2 - |x|^{-1}$, defined on $L^2 (R^3)$, in a constant magnetic field ${\\mathbf B}(h) = {\\mathbf \\nabla} \\times {\\mathbf A}(h)=(0,0,\\epsilon(h)B)$ in the weak field limit $\\epsilon(h) \\rightarrow 0$ as $h\\rightarrow{0}$. We consider the Planck's parameter $h$ t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06866","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"}