Semiclassical quantisation rules for the Dirac and Pauli equations
(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
- Keppeler, Stefan LU
- organization
- publishing date
- 2003
- 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
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Mathematical Physics (Faculty of Technology) (011040002)
- id
- a95ba38f-845b-48b6-b341-e677f62d7ac5 (old id 315587)
- date added to LUP
- 2016-04-01 11:36:22
- date last changed
- 2022-03-05 03:40:50
@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}}, doi = {{10.1016/S0003-4916(03)00007-1}}, volume = {{304}}, year = {{2003}}, }