dorsal/arxiv
View SchemaQuantum mechanics of an electron in a homogeneous magnetic field and a singular magnetic flux tube
| Authors | H. -P. Thienel |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9809047 |
| URL | https://arxiv.org/abs/quant-ph/9809047 |
| DOI | 10.1006/aphy.1999.5985 |
| Journal | Annals Phys. 280 (2000) 140-162 |
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.
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"abstract": "The eigenvalue problem of the Hamiltonian of an electron confined to a plane\nand subjected to a perpendicular time-independent magnetic field which is the\nsum of a homogeneous field and an additional field contributed by a singular\nflux tube, i.e. of zero width, is investigated. Since both a direct approach\nbased on distribution-valued operators and a limit process starting from a\nnon-singular flux tube, i.e. of finite size, fail, an alternative method is\napplied leading to consistent results. An essential feature is quantum\nmechanical supersymmetry at g=2 which imposes, by proper representation, the\ncorrect choice of \"boundary conditions\". The corresponding representation of\nthe Hilbert space in coordinate space differs from the usual space of\nsquare-integrable 2-spinors, entailing other unusual properties. The analysis\nis extended to $g\\ne 2$ so that supersymmetry is explicitly broken. Finally,\nthe singular Aharonov-Bohm system with the same amount of singular flux is\nanalysed by making use of the fact that the Hilbert space must be the same.",
"arxiv_id": "quant-ph/9809047",
"authors": [
"H. -P. Thienel"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1006/aphy.1999.5985",
"journal_ref": "Annals Phys. 280 (2000) 140-162",
"title": "Quantum mechanics of an electron in a homogeneous magnetic field and a singular magnetic flux tube",
"url": "https://arxiv.org/abs/quant-ph/9809047"
},
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