Quantum cylindrical integrability in magnetic fields

2022/10/07 by Ondřej Kubů, Kubů, O., L. Šnobl +1
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Neutrino Physics Research #Quantum Chromodynamics and Particle Interactions #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2210.03468

openalex publication_date 2022/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the classification of quadratically integrable systems of the cylindrical type with magnetic fields in quantum mechanics. Following the direct method used in classical mechanics by [F Fournier et al 2020 J. Phys. A: Math. Theor. 53 085203] to facilitate the comparison, the cases which may a priori differ yield 2 systems without any correction and 2 with it. In all of them, the magnetic field B coincides with the classical one, only the scalar potential W may contain a ℏ²-dependent correction. Two of the systems have both cylindrical integrals quadratic in momenta and are therefore not separable. These results form a basis for a prospective study of superintegrability.

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