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arXiv · 2603.23774

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

Daniel Burgarth·Paolo Facchi
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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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Daniel Burgarth, Paolo Facchi. 2026-03-24. The quantum harmonic oscillator on a circle -- fragmentation of the algebraic method. https://arxiv.org/abs/2603.23774

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