{"paper":{"title":"Coulomb plus power-law potentials in quantum mechanics","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Haken Ciftci, Qutaibeh D. Katatbeh, Richard L. Hall","submitted_at":"2003-05-08T16:21:27Z","abstract_excerpt":"We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \\ne 0. We show by envelope theory that the discrete eigenvalues E_{n\\ell} of H may be approximated by the semiclassical expression\n E_{n\\ell}(q) \\approx min_{r>0}\\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}.\n Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\\ell+1}e^{-(xr)^{q}}. We give detailed results for\n V(r) = -1/r + beta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0305018","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"}