The quantum harmonic oscillator on a circle -- fragmentation of the algebraic method
Quantum Physics
2026-03-26 v1
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.
Cite
@article{arxiv.2603.23774,
title = {The quantum harmonic oscillator on a circle -- fragmentation of the algebraic method},
author = {Daniel Burgarth and Paolo Facchi},
journal= {arXiv preprint arXiv:2603.23774},
year = {2026}
}
Comments
20 pages, 8 figures