{"paper":{"title":"Analysis of Schr\\\"odinger operators with inverse square potentials {II}: FEM and approximation of eigenfunctions in the periodic case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Eugenie Hunsicker, Hengguang Li, Victor Nistor, Ville Uski","submitted_at":"2012-05-10T00:11:48Z","abstract_excerpt":"Let $V$ be a {\\em periodic} potential on $\\RR^3$ that is smooth everywhere except at a discrete set $\\maS$ of points, where it has singularities of the form $Z/\\rho^2$, with $\\rho(x) = |x - p|$ for $x$ close to $p$ and $Z$ is continuous, $Z(p) > -1/4$ for $p \\in \\maS$. We also assume that $\\rho$ and $Z$ are smooth outside $\\maS$ and $Z$ is smooth in polar coordinates around each singular point. Let us denote by $\\Lambda$ the periodicity lattice and set $\\TT := \\RR^3/ \\Lambda$. In the first paper of this series \\cite{HLNU1}, we obtained regularity results in weighted Sobolev space for the eigen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2127","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"}