Physics – Quantum Physics
Scientific paper
1998-09-16
Annals Phys. 280 (2000) 140-162
Physics
Quantum Physics
23 pages, LaTeX, minor changes
Scientific paper
10.1006/aphy.1999.5985
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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