{"paper":{"title":"A Moments' Analysis of Quasi-Exactly Solvable Systems: A New Perspective on the Sextic Anharmonic and Bender-Dunne Potentials","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Carlos R. Handy, Daniel Vrinceanu, Rahul Gupta","submitted_at":"2014-02-24T15:56:56Z","abstract_excerpt":"There continues to be great interest in understanding quasi-exactly solvable (QES) systems. In one dimension, QES states assume the form $\\Psi(x) =x^\\gamma P_d(x) {\\cal A}(x)$, where ${\\cal A}(x) > 0$ is known in closed form, and $P_d(x)$ is a polynomial to be determined. That is ${{\\Psi(x)}\\over {x^\\gamma{\\cal A}(x)}} = \\sum_{n=0}^\\infty a_nx^n$ truncates. The extension of this \"truncation\" procedure to non-QES states corresponds to the Hill determinant method, which is unstable when the {\\it reference} function assumes the physical asymptotic form. Recently, Handy and Vrinceanu introduced th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5868","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"}