圆柱体上的朗道电子问题
The Landau electron problem on a cylinder
摘要：
本文研究了在均匀径向磁场作用下，电子在无限长圆柱上运动的量子力学。这个问题在某些方面与无限平面上的相应问题非常相似。然而，与平面不同的是，磁场的对称性组，即绕轴的旋转和轴向平移，{ \em not}由量子电子实现，而只有一个包括沿轴向方向的旋转和离散平移的子群。离散平移的基本步长是这样的，即通过“单位圆柱胞”的通量以通量量子为单位进行量子化。结果是在两种不同的方式得出：使用条件的对称群的投影实现和使用更熟悉的方法来确定一个给定的哈密顿量的对称性。
英文摘要：
We consider the quantum mechanics of an electron confined to move on an infinite cylinder in the presence of a uniform radial magnetic field. This problem is in certain ways very similar to the corresponding problem on the infinite plane. Unlike the plane however, the group of symmetries of the magnetic field, namely, rotations about the axis and the axial translations, is {\em not} realized by the quantum electron but only a subgroup comprising rotations and discrete translations along the axial direction, is. The basic step size of discrete translations is such that the flux through the `unit cylinder cell' is quantized in units of the flux quantum. The result is derived in two different ways: using the condition of projective realization of symmetry groups and using the more familiar approach of determining the symmetries of a given Hamiltonian.
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