Published December 12, 2012
| Version Supplemental Material + Published
Journal Article
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Propagation of a relativistic electron wave packet in the Dirac equation
Abstract
Solving the Dirac equation is a formidable task due to the high frequency and the degrees of freedom involved. However, this high frequency allows one to obtain an approximation to the equation. Here, we directly solve the Dirac equation using an envelope method and derive analytical solutions of Dirac wave packets to first order for the small momentum spread. We apply the insight gained from this solution to the Zitterbewegung behavior in a Dirac-like system, where we show that it is crucial to include the first-order term in our solution to correctly describe a Dirac packet.
Additional Information
© 2012 American Physical Society. Received 10 September 2012; published 12 December 2012. This work was supported by the National Science Foundation and the Air Force Office of Scientific Research in the Center for Physical Biology funded by the Gordon and Betty Moore Foundation. The author is grateful to Professor A. H. Zewail for his support. The author also would like to thank Jessica A. Pfeilsticker for the helpful discussion.Attached Files
Published - PhysRevA.86.062105.pdf
Supplemental Material - README.TXT
Supplemental Material - zitterbewegung.avi
Supplemental Material - zitterbewegung_supporting.pdf
Files
PhysRevA.86.062105.pdf
Additional details
Identifiers
- Eprint ID
- 36028
- Resolver ID
- CaltechAUTHORS:20121218-090706692
Funding
- NSF
- Air Force Office of Scientific Research (AFOSR)
- Gordon and Betty Moore Foundation
Dates
- Created
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2012-12-18Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field