{"paper":{"title":"The $q$-deformed Schr\\\"odinger Equation of the Harmonic Oscillator on the Quantum Euclidian Space","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Satoshi Watamura, Ursula Carow-Watamura","submitted_at":"1993-10-01T02:15:07Z","abstract_excerpt":"We consider the $q$-deformed Schr\\\"odinger equation of the harmonic oscillator on the $N$-dimensional quantum Euclidian space. The creation and annihilation operator are found, which systematically produce all energy levels and eigenfunctions of the Schr\\\"odinger equation. In order to get the $q$-series representation of the eigenfunction, we also give an alternative way to solve the Schr\\\"odinger equation which is based on the $q$-analysis. We represent the Schr\\\"odinger equation by the $q$-difference equation and solve it by using $q$-polynomials and $q$-exponential functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9309160","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"}