{"paper":{"title":"Soft-core Coulomb potentials and Heun's differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.atom-ph","physics.chem-ph"],"primary_cat":"math-ph","authors_text":"K. D. Sen, Nasser Saad, Richard L. Hall","submitted_at":"2009-12-17T15:53:45Z","abstract_excerpt":"Schroedinger's equation with the attractive potential\n  V(r) = -Z/(r^q+ b^q)^(1/q), Z > 0, b > 0, q >= 1, is shown, for general values of the parameters Z and b, to be reducible to the confluent Heun equation in the case q=1, and to the generalized Heun equation in case q=2. In a formulation with correct asymptotics, the eigenstates are specified a priori up to an unknown factor. In certain special cases this factor becomes a polynomial. The Asymptotic Iteration Method is used either to find the polynomial factor and the associated eigenvalue explicitly, or to construct accurate approximations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3445","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"}