VLSI Design

VLSI Design / 1999 / Article
Special Issue

International Workshop on Quantum Theory

View this Special Issue

Open Access

Volume 9 |Article ID 089476 | https://doi.org/10.1155/1999/89476

Norbert J. Mauser, "Rigorous Derivation of the Pauli Equation With Time-dependent Electromagnetic Field", VLSI Design, vol. 9, Article ID 089476, 12 pages, 1999. https://doi.org/10.1155/1999/89476

Rigorous Derivation of the Pauli Equation With Time-dependent Electromagnetic Field

Received13 Aug 1997
Revised01 Dec 1998

Abstract

In this work we discuss relativistic corrections for the description of charge carriers in a quantum mechanical framework. The fundamental equation is the Dirac equation which takes into account also the electron's spin. However, this equation intrinsically also incorporates positrons which play no role in applications in solid state physics. We give a rigorous derivation of the Pauli equation describing electrons in a first order approximation of the Dirac equation in the limit of infinite velocity of light. We deal with time-dependent electromagnetic potentials where no rigorous results have been given before. Our approach is based on the use of appropriate projection operators for the electron and the positron component of the spinor which are better suited than the widely used simple splitting into ‘upper (large)’ and ‘lower (small) component’. We also systematically derive corrections at second order in 1/c where we essentially recover the results of the Foldy-Wouthuysen approach. However, due to the non-static problem, differences occur in the term which couples the electric field with the spin.

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views384
Downloads790
Citations

Article of the Year Award: Outstanding research contributions of 2020, as selected by our Chief Editors. Read the winning articles.