The quantum harmonic oscillator on a circle -- fragmentation of the algebraic method

Quantum Physics [Submitted on 24 Mar 2026] The quantum harmonic oscillator on a circle -- fragmentation of the algebraic method Daniel Burgarth, Paolo Facchi A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This raises the question where the usual algebraic argument -- implying integer gaps -- fails. The answer is illuminating and covers a surprisingly rich range of physical phenomena for such a simple model. Comments: 20 pages, 8 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.23774 [quant-ph]   (or arXiv:2603.23774v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.23774 Focus to learn more Submission history From: Daniel Burgarth [view email] [v1] Tue, 24 Mar 2026 23:13:17 UTC (845 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)