{"paper":{"title":"Exact normalized eigenfunctions for general deformed Hulth\\'en potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"K. D. Sen, Nasser Saad, Richard L. Hall","submitted_at":"2018-12-16T03:16:12Z","abstract_excerpt":"The exact solutions of Schr\\\"odinger's equation with the deformed Hulth\\'en potential $V_q(x)=-{\\mu\\, e^{-\\delta\\,x }}/({1-q\\,e^{-\\delta\\,x}}),~ \\delta,\\mu, q>0$ are given, along with a closed--form formula for the normalization constants of the eigenfunctions for arbitrary $q>0$. The Crum-Darboux transformation is then used to derive the corresponding exact solutions for the extended Hulth\\'en potentials $V(x)= -{\\mu\\, e^{-\\delta\\,x }}/({1-q\\,e^{-\\delta\\,x}})+ {q\\,j(j+1)\\, e^{-\\delta\\,x }}/({1-q\\,e^{-\\delta\\,x}})^2, j=0,1,2,\\dots.$ A general formula for the new normalization condition is also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06383","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"}