SciPost logo

Quantum cylindrical integrability in magnetic fields

Ondřej Kubů, Libor Šnobl

SciPost Phys. Proc. 14, 032 (2023) · published 24 November 2023

Proceedings event

34th International Colloquium on Group Theoretical Methods in Physics


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 $\hbar^2$-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.

Cited by 1

Crossref Cited-by

Authors / Affiliation: mappings to Contributors and Organizations

See all Organizations.
Funders for the research work leading to this publication