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

• URL: http://arxiv.org/abs/2603.23774v1
• Date: Tue, 24 Mar 2026 23:13:17 GMT
• Title: The quantum harmonic oscillator on a circle -- fragmentation of the algebraic method
• Abstract summary: A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic.<n>This raises the question where the usual algebraic argument -- implying integer gaps -- fails.<n>The answer is illuminating and covers a surprisingly rich range of physical phenomena for such a simple model.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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