dorsal/arxiv
View SchemaSemiclassical quantisation rules for the Dirac and Pauli equations
| Authors | Stefan Keppeler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0212082 |
| URL | https://arxiv.org/abs/quant-ph/0212082 |
| DOI | 10.1016/S0003-4916(03)00007-1 |
| Journal | Ann. Phys. (NY) 304 (2003) 40-71 |
Abstract
We derive explicit semiclassical quantisation conditions for the Dirac and Pauli equations. We show that the spin degree of freedom yields a contribution which is of the same order of magnitude as the Maslov correction in Einstein-Brillouin-Keller quantisation. In order to obtain this result a generalisation of the notion of integrability for a certain skew product flow of classical translational dynamics and classical spin precession has to be derived. Among the examples discussed is the relativistic Kepler problem with Thomas precession, whose treatment sheds some light on the amazing success of Sommerfeld's theory of fine structure [Ann. Phys. (Leipzig) 51 (1916) 1--91].
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"abstract": "We derive explicit semiclassical quantisation conditions for the Dirac and\nPauli equations. We show that the spin degree of freedom yields a contribution\nwhich is of the same order of magnitude as the Maslov correction in\nEinstein-Brillouin-Keller quantisation. In order to obtain this result a\ngeneralisation of the notion of integrability for a certain skew product flow\nof classical translational dynamics and classical spin precession has to be\nderived. Among the examples discussed is the relativistic Kepler problem with\nThomas precession, whose treatment sheds some light on the amazing success of\nSommerfeld\u0027s theory of fine structure [Ann. Phys. (Leipzig) 51 (1916) 1--91].",
"arxiv_id": "quant-ph/0212082",
"authors": [
"Stefan Keppeler"
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"doi": "10.1016/S0003-4916(03)00007-1",
"journal_ref": "Ann. Phys. (NY) 304 (2003) 40-71",
"title": "Semiclassical quantisation rules for the Dirac and Pauli equations",
"url": "https://arxiv.org/abs/quant-ph/0212082"
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