{"paper":{"title":"The H$_2^+$ molecular ion: a solution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.atom-ph"],"primary_cat":"quant-ph","authors_text":"Alexander V. Turbiner, Horacio Olivares-Pil\\'on","submitted_at":"2011-03-25T15:03:28Z","abstract_excerpt":"Combining the WKB expansion at large distances and Perturbation Theory at small distances it is constructed a compact uniform approximation for eigenfunctions. For lowest states $1s\\si_{g}$ and $2p\\si_{u}$ this approximation provides the relative accuracy $\\lesssim 10^{-5}$ (5 s.d.) for any real $x$ in eigenfunctions and for total energy $E(R)$ it gives 10-11 s.d. for internuclear distances $R \\in [0,50]$. Corrections to proposed approximations are evaluated. Separation constants and the oscillator strength for the transition $1s\\si_{g} \\rar 2p\\si_{u}$ are calculated and compared with existing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4989","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"}