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Quantum mechanics of an electron in a homogeneous magnetic field and a
singular magnetic flux tube
H. -P. Thienel
abstract: 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/9809047
- categories:
- quant-ph cond-mat.mes-hall hep-th math-ph math.MP
- comments:
- 23 pages, LaTeX, minor changes
- doi:
- 10.1006/aphy.1999.5985
- arxiv_id:
- quant-ph/9809047
- journal_ref:
- Annals Phys. 280 (2000) 140-162
- report_no:
- Si-98-9
- created:
- 1998-09-16
- updated:
- 2000-06-01
Full article ▸
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