{"paper":{"title":"Deformed su(1,1) Algebra as a Model for Quantum Oscillators","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP","math.RT","quant-ph"],"primary_cat":"math-ph","authors_text":"Elchin I. Jafarov, Joris Van der Jeugt, Neli I. Stoilova","submitted_at":"2012-02-16T09:31:06Z","abstract_excerpt":"The Lie algebra $\\mathfrak{su}(1,1)$ can be deformed by a reflection operator, in such a way that the positive discrete series representations of $\\mathfrak{su}(1,1)$ can be extended to representations of this deformed algebra $\\mathfrak{su}(1,1)_\\gamma$. Just as the positive discrete series representations of $\\mathfrak{su}(1,1)$ can be used to model a quantum oscillator with Meixner-Pollaczek polynomials as wave functions, the corresponding representations of $\\mathfrak{su}(1,1)_\\gamma$ can be utilized to construct models of a quantum oscillator. In this case, the wave functions are expresse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3541","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"}