{"paper":{"title":"Energies and wave functions for a soft-core Coulomb potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.atom-ph","quant-ph"],"primary_cat":"math-ph","authors_text":"Hakan Ciftci, K. D. Sen, Nasser Saad, Richard L. Hall","submitted_at":"2009-08-14T16:12:36Z","abstract_excerpt":"For the family of model soft Coulomb potentials represented by V(r) = -\\frac{Z}{(r^q+\\beta^q)^{\\frac{1}{q}}}, with the parameters\n  Z>0, \\beta>0, q \\ge 1, it is shown analytically that the potentials and eigenvalues, E_{\\nu\\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{\\nu\\ell} and corresponding wave functions, expressed in terms of Z and \\beta. A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2087","kind":"arxiv","version":2},"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"}