Exact solution of the Zeeman effect in singleelectron systems
(2005) In Physica Scripta T120. p.9098 Abstract
 Contrary to popular belief, the Zeeman effect can be treated exactly in singleelectron systems, for arbitrary magnetic field strengths, as long as the term quadratic in the magnetic field can be ignored. These formulas were actually derived already around 1927 by Darwin, using the classical picture of angular momentum, and presented in their proper quantum mechanical form in 1933 by Bethe, although without any proof. The expressions have since been more or less lost from the literature; instead, the conventional treatment nowadays is to present only the approximations for weak and strong fields, respectively. However, in fusion research and other plasma physics applications, the magnetic fields applied to control the shape and position... (More)
 Contrary to popular belief, the Zeeman effect can be treated exactly in singleelectron systems, for arbitrary magnetic field strengths, as long as the term quadratic in the magnetic field can be ignored. These formulas were actually derived already around 1927 by Darwin, using the classical picture of angular momentum, and presented in their proper quantum mechanical form in 1933 by Bethe, although without any proof. The expressions have since been more or less lost from the literature; instead, the conventional treatment nowadays is to present only the approximations for weak and strong fields, respectively. However, in fusion research and other plasma physics applications, the magnetic fields applied to control the shape and position of the plasma span the entire region from weak to strong fields, and there is a need for a unified treatment. In this paper we present the detailed quantum mechanical derivation of the exact eigenenergies and eigenstates of hydrogenlike atoms and ions in a static magnetic. eld. Notably, these formulas are not much more complicated than the betterknown approximations. Moreover, the derivation allows the value of the electron spin gyromagnetic ratio g(s) to be different from 2. For completeness, we then review the details of dipole transitions between two hydrogenic levels, and calculate the corresponding Zeeman spectrum. The various approximations made in the derivation are also discussed in details. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/208459
 author
 Blom, Anders ^{LU}
 organization
 publishing date
 2005
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Physica Scripta
 volume
 T120
 pages
 90  98
 publisher
 IOP Publishing
 external identifiers

 wos:000236907000016
 scopus:42349083502
 ISSN
 00318949
 DOI
 10.1088/00318949/2005/T120/014
 language
 English
 LU publication?
 yes
 id
 ed237ed435d0471d8f2474a5e801205c (old id 208459)
 date added to LUP
 20160401 12:26:16
 date last changed
 20210908 01:09:32
@article{ed237ed435d0471d8f2474a5e801205c, abstract = {Contrary to popular belief, the Zeeman effect can be treated exactly in singleelectron systems, for arbitrary magnetic field strengths, as long as the term quadratic in the magnetic field can be ignored. These formulas were actually derived already around 1927 by Darwin, using the classical picture of angular momentum, and presented in their proper quantum mechanical form in 1933 by Bethe, although without any proof. The expressions have since been more or less lost from the literature; instead, the conventional treatment nowadays is to present only the approximations for weak and strong fields, respectively. However, in fusion research and other plasma physics applications, the magnetic fields applied to control the shape and position of the plasma span the entire region from weak to strong fields, and there is a need for a unified treatment. In this paper we present the detailed quantum mechanical derivation of the exact eigenenergies and eigenstates of hydrogenlike atoms and ions in a static magnetic. eld. Notably, these formulas are not much more complicated than the betterknown approximations. Moreover, the derivation allows the value of the electron spin gyromagnetic ratio g(s) to be different from 2. For completeness, we then review the details of dipole transitions between two hydrogenic levels, and calculate the corresponding Zeeman spectrum. The various approximations made in the derivation are also discussed in details.}, author = {Blom, Anders}, issn = {00318949}, language = {eng}, pages = {9098}, publisher = {IOP Publishing}, series = {Physica Scripta}, title = {Exact solution of the Zeeman effect in singleelectron systems}, url = {http://dx.doi.org/10.1088/00318949/2005/T120/014}, doi = {10.1088/00318949/2005/T120/014}, volume = {T120}, year = {2005}, }