{"paper":{"title":"Quantum confinement on non-complete Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","math.SP"],"primary_cat":"math.DG","authors_text":"Dario Prandi, Luca Rizzi, Marcello Seri","submitted_at":"2016-09-06T20:00:03Z","abstract_excerpt":"We consider the quantum completeness problem, i.e. the problem of confining quantum particles, on a non-complete Riemannian manifold $M$ equipped with a smooth measure $\\omega$, possibly degenerate or singular near the metric boundary of $M$, and in presence of a real-valued potential $V\\in L^2_{\\mathrm{loc}}(M)$. The main merit of this paper is the identification of an intrinsic quantity, the effective potential $V_{\\mathrm{eff}}$, which allows to formulate simple criteria for quantum confinement. Let $\\delta$ be the distance from the possibly non-compact metric boundary of $M$. A simplified "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01724","kind":"arxiv","version":3},"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"}