{"paper":{"title":"The $SO_q(N,{\\bf R})$-Symmetric Harmonic Oscillator on the Quantum Euclidean Space ${\\bf R}_q^N$ and its Hilbert Space Structure","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Gaetano Fiore","submitted_at":"1993-06-04T18:05:58Z","abstract_excerpt":"We show that the isotropic harmonic oscillator in the ordinary euclidean space ${\\bf R}^N$ ($N\\ge 3$) admits a natural q-deformation into a new quantum mechanical model having a q-deformed symmetry (in the sense of quantum groups), $SO_q(N,{\\bf R})$. The q-deformation is the consequence of replacing $ R^N$ by ${\\bf R}^N_q$ (the corresponding quantum space). This provides an example of quantum mechanics on a noncommutative geometrical space. To reach the goal, we also have to deal with a sensible definition of integration over ${\\bf R}^N_q$, which we use for the definition of the scalar product"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9306030","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"}