{"paper":{"title":"Upper limit on the number of bound states of the spinless Salpeter equation","license":"","headline":"","cross_cats":["math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"Fabian Brau","submitted_at":"2004-01-12T11:36:15Z","abstract_excerpt":"We obtain, using the Birman-Schwinger method, upper limits on the total number of bound states and on the number of $\\ell$-wave bound states of the semirelativistic spinless Salpeter equation. We also obtain a simple condition, in the ultrarelativistic case ($m=0$), for the existence of at least one $\\ell$-wave bound states: $C(\\ell,p/(p-1))$ $\\int_0^{\\infty}dr r^{p-1} |V^-(r)|^p\\ge 1$, where $C(\\ell,p/(p-1))$ is a known function of $\\ell$ and $p>1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0401022","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"}