电子在均匀磁场和奇异磁通量管中的量子力学
Quantum mechanics of an electron in a homogeneous magnetic field and a singular magnetic flux tube
摘要：
本文研究了平面电子在与时间无关的垂直磁场作用下的哈密顿量的本征值问题，磁场是均匀场和由零宽度奇异磁通管贡献的附加场之和。由于一个直接的方法的基础上的分布值的运营商和一个极限过程从一个非奇异的通量管，即有限的大小，失败，一个替代的方法是适用于导致一致的结果。一个基本特征是g=2的量子力学超对称性，通过适当的表示，它可以正确选择“边界条件”。希尔伯特空间在坐标空间中的相应表示不同于通常的平方可积2-旋量空间，包含其他不寻常的性质。分析扩展到$g\ne 2$，使超对称性明确破缺。最后，利用Hilbert空间必须相同的事实，分析了具有相同奇异通量的奇异Aharonov-Bohm系统。
英文摘要：
The eigenvalue problem of the Hamiltonian of an electron confined to a plane and subjected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux tube, i.e. of zero width, is investigated. Since both a direct approach based on distribution-valued operators and a limit process starting from a non-singular flux tube, i.e. of finite size, fail, an alternative method is applied leading to consistent results. An essential feature is quantum mechanical supersymmetry at g=2 which imposes, by proper representation, the correct choice of "boundary conditions". The corresponding representation of the Hilbert space in coordinate space differs from the usual space of square-integrable 2-spinors, entailing other unusual properties. The analysis is extended to $g\ne 2$ so that supersymmetry is explicitly broken. Finally, the singular Aharonov-Bohm system with the same amount of singular flux is analysed by making use of the fact that the Hilbert space must be the same.
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