{"paper":{"title":"Classical-quantum correspondence for shape-invariant systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. M. Grundland, D. Riglioni","submitted_at":"2014-05-05T17:16:57Z","abstract_excerpt":"A quantization procedure, which has recently been introduced for the analysis of Painlev\\'e equations, is applied to a general time-independent potential of a Newton equation. This analysis shows that the quantization procedure preserves the exact solvability property for the class of shape-invariant potentials. When a general potential is considered the quantization procedure involves the solution of a Gambier XXVII transcendental equation. Explicit examples involving classical and exceptional orthogonal Laguerre and Jacobi polynomials are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0968","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"}