TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.14.032
TI  - Quantum cylindrical integrability in magnetic fields
PY  - 2023/11/24
UR  - https://scipost.org/SciPostPhysProc.14.032
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 14
SP  - 032
A1  - Kubů, Ondřej
AU  - Šnobl, Libor
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysProc.14.032,
	title={{Quantum cylindrical integrability in magnetic fields}},
	author={Ondřej Kubů and Libor Šnobl},
	journal={SciPost Phys. Proc.},
	pages={032},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.14.032},
	url={https://scipost.org/10.21468/SciPostPhysProc.14.032},
}