Exact solution of the Zeeman effect in single-electron systems
(2005) In Physica Scripta T120. p.90-98- Abstract
- Contrary to popular belief, the Zeeman effect can be treated exactly in single-electron 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 single-electron 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 hydrogen-like atoms and ions in a static magnetic. eld. Notably, these formulas are not much more complicated than the better-known 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
- 0031-8949
- DOI
- 10.1088/0031-8949/2005/T120/014
- language
- English
- LU publication?
- yes
- id
- ed237ed4-35d0-471d-8f24-74a5e801205c (old id 208459)
- date added to LUP
- 2016-04-01 12:26:16
- date last changed
- 2022-01-27 03:44:03
@article{ed237ed4-35d0-471d-8f24-74a5e801205c,
abstract = {{Contrary to popular belief, the Zeeman effect can be treated exactly in single-electron 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 hydrogen-like atoms and ions in a static magnetic. eld. Notably, these formulas are not much more complicated than the better-known 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 = {{0031-8949}},
language = {{eng}},
pages = {{90--98}},
publisher = {{IOP Publishing}},
series = {{Physica Scripta}},
title = {{Exact solution of the Zeeman effect in single-electron systems}},
url = {{http://dx.doi.org/10.1088/0031-8949/2005/T120/014}},
doi = {{10.1088/0031-8949/2005/T120/014}},
volume = {{T120}},
year = {{2005}},
}