Quantum cylindrical integrability in magnetic fields
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...
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| Format: | Article |
| Language: | English |
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SciPost
2023-11-01
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| Series: | SciPost Physics Proceedings |
| Online Access: | https://scipost.org/SciPostPhysProc.14.032 |
| Summary: | 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. |
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| ISSN: | 2666-4003 |