The quantum harmonic oscillator on a circle -- fragmentation of the algebraic method
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866917360863019008 |
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| author | Burgarth, Daniel Facchi, Paolo |
| author_facet | Burgarth, Daniel Facchi, Paolo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23774 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The quantum harmonic oscillator on a circle -- fragmentation of the algebraic method Burgarth, Daniel Facchi, Paolo Quantum Physics 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. |
| title | The quantum harmonic oscillator on a circle -- fragmentation of the algebraic method |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.23774 |