{"paper":{"title":"On the bound states of the discrete Schr\\\"odinger equation with compactly supported potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Abdon E. Choque-Rivero, Tuncay Aktosun, Vassilis G. Papanicolaou","submitted_at":"2018-09-21T14:42:13Z","abstract_excerpt":"The discrete Schr\\\"odinger operator with the Dirichlet boundary condition is considered on the half-line lattice $n\\in \\{1,2,3,\\dots\\}.$ It is assumed that the potential belongs to class $\\mathcal A_b,$ i.e. it is real valued, vanishes when $n>b$ with $b$ being a fixed positive integer, and is nonzero at $n=b.$ The proof is provided to show that the corresponding number of bound states, $N,$ must satisfy the inequality $0\\le N\\le b.$ It is shown that for each fixed nonnegative integer $k$ in the set $\\{0,1,2,\\dots,b\\},$ there exist infinitely many potentials in class $\\mathcal A_b$ for which t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08150","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"}