• Media type: Text; E-Article
  • Title: How to approximate the Dirac equation with the Mauser method
  • Contributor: Renziehausen, Klaus [Author]; Liu, Kunlong [Author]; Barth, Ingo [Author]
  • Published: Digital Library Thüringen, 2022-08
  • Language: English
  • DOI: https://doi.org/10.1007/s40509-022-00270-4
  • Keywords: Quantum mechanics ; Dirac equation ; Relativistic physics ; ScholarlyArticle ; article ; Atomic physics
  • Origination:
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  • Description: Mauser and coworkers discussed in a series of papers an ansatz how to split the Dirac equation and the wave function appearing therein into a part related to a free moving electron and another part related to a free moving positron. This ansatz includes an expansion of these quantities into orders of the reciprocal of the speed of light ϵ = 1 / c \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon = 1/c$$\end{document} . In particular, in Mauser (VLSI Design 9:415, 1999) it is discussed how to apply this expansion up to the second order in the reciprocal of the speed of light ϵ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document} . As an expansion of this analysis, we show in this work how all three well-known terms that appear in an expansion of the Dirac equation in second order on the reciprocal of the speed of light, namely, a relativistic correction to the kinetic energy, the Darwin term, and the spin-orbit interaction, can be found using the ansatz of Mauser—and doing so, we close a gap between this ansatz to approximate the Dirac equation and other approximative results found using the Foldy–Wouthuysen transformation.
  • Access State: Open Access
  • Rights information: Attribution (CC BY)