The DOI matches its Crossref record; 34 of the 34 references it cites were found in a registry or an index.
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.
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“Initial states with px = 0, or localized wave packets, follow more complex trajectories [25].”
From Direct observation of zitterbewegung in a Bose–Einstein condensate (2013) · cites this paper as [25]
Citations
Cites
The quantum theory of the electron
Dirac, P. A. M. (1928) · Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1928.0023 · Cited by 3,657
Relativistic Quantum Mechanics
Bjorken, J. D., Drell, S. D., & Mansfield, J. E. (1965) · Physics Today · doi:10.1063/1.3047288 · Cited by 2,836
On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit
Foldy, L. L., & Wouthuysen, S. A. (1950) · Physical Review · doi:10.1103/physrev.78.29 · Cited by 2,183
Sakurai, J. J., & Freedman, D. Z. (1968) · American Journal of Physics · doi:10.1119/1.1974573 · Cited by 2,022
Thaller, B. (1992) · doi:10.1007/978-3-662-02753-0 · Cited by 1,530
Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac
Klein, O. (1929) · Zeitschrift f�r Physik · doi:10.1007/bf01339716 · Cited by 1,080
Anderson, C. D. (1933) · Physical Review · doi:10.1103/physrev.43.491 · Cited by 779
Quantum simulation of the Dirac equation
Gerritsma, R., Kirchmair, G., Zähringer, F., Solano, E., Blatt, R., & Roos, C. F. (2010) · Nature · doi:10.1038/nature08688 · Cited by 725
Relativistic Quantum Mechanics
Greiner, W. (1995) · doi:10.1007/978-3-642-88082-7 · Cited by 502
The wave equations of the electron
Darwin, C. G. (1928) · Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1928.0076 · Cited by 472
Research works printed but not linked: 2
- E. Schrödinger, 1930, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl., 24, 418
- N. Hamdan, 2007, Proc. Pak. Acad. Sci., 44, 263
Cited by
Direct observation of zitterbewegung in a Bose–Einstein condensate
LeBlanc, L. J., Beeler, M. C., Jiménez-García, K., Perry, A. R., Sugawa, S., Williams, R. A., & Spielman, I. B. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/7/073011 · Cited by 186
Metadata
- Authors
- Park, S. T.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2012-12-12
- Volume
- 86
- Issue
- 6
- ISSN
- 1050-2947
- 1094-1622
- Cited by
- 22
- References
- 34
- Language
- en
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- Park, S. T. (2012). Propagation of a relativistic electron wave packet in the Dirac equation. Physical Review A. https://doi.org/10.1103/physreva.86.062105
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