论文标题
磁场中的量子圆柱可合性性
Quantum cylindrical integrability in magnetic fields
论文作者
论文摘要
我们介绍了量子力学中具有磁场的圆柱类型的四型整合系统的分类。遵循经典力学中使用的直接方法，由[F Fournier等人2020 J. Phys。答：数学。理论。 53 085203]为了促进比较，可能先验的案例差异差异2系统，而没有任何校正和2个系统。在所有这些中，磁场$ b $与经典的磁场相吻合，只有标量势$ w $可能包含$ \ hbar^2 $依赖性校正。其中两个系统在动量中具有二次圆柱积分二次，因此不可分开。这些结果构成了前瞻性研究的基础。
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.
