{"paper":{"title":"The $d$-dimensional softcore Coulomb potential and the generalized confluent Heun equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Kyle R. Bryenton, Nasser Saad, Richard L Hall","submitted_at":"2018-10-15T17:42:01Z","abstract_excerpt":"An analysis of the generalized confluent Heun equation $(\\alpha_2r^2+\\alpha_1r)\\,y''+(\\beta_2r^2+\\beta_1r+\\beta_0)\\,y'-(\\varepsilon_1r+\\varepsilon_0)\\,y=0$ in $d$-dimensional space, where $\\{\\alpha_i, \\beta_i, \\varepsilon_i\\}$ are real parameters, is presented. With the aid of these general results, the quasi exact solvability of the Schr\\\"odinger eigenproblem generated by the softcore Coulomb potential $V(r)=-e^2Z/(r+b),\\, b>0$, is explicitly resolved. Necessary and sufficient conditions for polynomial solvability are given. A three-term recurrence relation is provided to generate the coeffic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06539","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"}