{"paper":{"title":"Formula Method for Bound State Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Babatunde J. Falaye, Majid Hamzavi, Sameer M. Ikhdair","submitted_at":"2014-08-15T12:50:24Z","abstract_excerpt":"We present a simple formula for finding bound state solution of any quantum wave equation which can be simplified to the form of $\\Psi\"(s)+\\frac{(k_1-k_2s)}{s(1-k_3s)}\\Psi'(s)+\\frac{(As^2+Bs+C)}{s^2(1-k_3s)^2}\\Psi(s)=0$. The two cases where $k_3=0$ and $k_3\\neq 0$ are studied. We derive an expression for the energy spectrum and the wave function in terms of generalized hypergeometric functions $_2F_1(\\alpha, \\beta; \\gamma; k_3s)$. In order to show the accuracy of this proposed formula, we resort to obtaining bound state solutions for some existing eigenvalue problems in a rather more simplifie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3523","kind":"arxiv","version":4},"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"}