The Dirac Equation in the Low Energy Limit
The purpose of this work is to give an introduction to relativistic quantum mechanics for the electron. First a review of the Dirac equation and its application to a free electron and an electron in an electromagnetic field will be given. In particular the hydrogen atom is studied. The low energy li...
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Umeå universitet, Institutionen för fysik
2016
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ndltd-UPSALLA1-oai-DiVA.org-umu-1305172017-01-21T05:34:39ZThe Dirac Equation in the Low Energy LimitengLinder, BjörnUmeå universitet, Institutionen för fysik2016The purpose of this work is to give an introduction to relativistic quantum mechanics for the electron. First a review of the Dirac equation and its application to a free electron and an electron in an electromagnetic field will be given. In particular the hydrogen atom is studied. The low energy limit and the lowest order corrections to non-relativistic quantum mechanics are investigated. These corrections include, among others, the gyromagnetic ratio of the electron and spin-orbit coupling in the hydrogen atom. The low energy limit will be studied both in the usual Pauli-Dirac representation and by using the Foldy-Wouthuysen transformation. The Pauli-Dirac representation is used to obtain the correction terms for the energy levels in the hydrogen atom. The Foldy-Wouthuysen transformation is applied to obtain the corresponding Hamiltonian corrections to order α4 . Student thesisinfo:eu-repo/semantics/bachelorThesistexthttp://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-130517application/pdfinfo:eu-repo/semantics/openAccess |
| collection |
NDLTD |
| language |
English |
| format |
Others
|
| sources |
NDLTD |
| description |
The purpose of this work is to give an introduction to relativistic quantum mechanics for the electron. First a review of the Dirac equation and its application to a free electron and an electron in an electromagnetic field will be given. In particular the hydrogen atom is studied. The low energy limit and the lowest order corrections to non-relativistic quantum mechanics are investigated. These corrections include, among others, the gyromagnetic ratio of the electron and spin-orbit coupling in the hydrogen atom. The low energy limit will be studied both in the usual Pauli-Dirac representation and by using the Foldy-Wouthuysen transformation. The Pauli-Dirac representation is used to obtain the correction terms for the energy levels in the hydrogen atom. The Foldy-Wouthuysen transformation is applied to obtain the corresponding Hamiltonian corrections to order α4 . |
| author |
Linder, Björn |
| spellingShingle |
Linder, Björn The Dirac Equation in the Low Energy Limit |
| author_facet |
Linder, Björn |
| author_sort |
Linder, Björn |
| title |
The Dirac Equation in the Low Energy Limit |
| title_short |
The Dirac Equation in the Low Energy Limit |
| title_full |
The Dirac Equation in the Low Energy Limit |
| title_fullStr |
The Dirac Equation in the Low Energy Limit |
| title_full_unstemmed |
The Dirac Equation in the Low Energy Limit |
| title_sort |
dirac equation in the low energy limit |
| publisher |
Umeå universitet, Institutionen för fysik |
| publishDate |
2016 |
| url |
http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-130517 |
| work_keys_str_mv |
AT linderbjorn thediracequationinthelowenergylimit AT linderbjorn diracequationinthelowenergylimit |
| _version_ |
1718410086777356288 |