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Semiclassical quantisation rules for the Dirac and Pauli equations

Keppeler, Stefan LU (2003) In Annals of Physics 304(1). p.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]. (C) 2003 Elsevier Science (USA). All rights reserved.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Annals of Physics
volume
304
issue
1
pages
40 - 71
publisher
Elsevier
external identifiers
  • wos:000181776100003
  • scopus:0037354623
ISSN
0003-4916
DOI
10.1016/S0003-4916(03)00007-1
language
English
LU publication?
yes
id
a95ba38f-845b-48b6-b341-e677f62d7ac5 (old id 315587)
date added to LUP
2007-09-16 07:25:15
date last changed
2018-05-29 11:21:44
@article{a95ba38f-845b-48b6-b341-e677f62d7ac5,
  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]. (C) 2003 Elsevier Science (USA). All rights reserved.},
  author       = {Keppeler, Stefan},
  issn         = {0003-4916},
  language     = {eng},
  number       = {1},
  pages        = {40--71},
  publisher    = {Elsevier},
  series       = {Annals of Physics},
  title        = {Semiclassical quantisation rules for the Dirac and Pauli equations},
  url          = {http://dx.doi.org/10.1016/S0003-4916(03)00007-1},
  volume       = {304},
  year         = {2003},
}