Zitterbewegung

In physics, the zitterbewegung (German pronunciation: [ˈtsɪtɐ.bəˌveːɡʊŋ], from German zittern 'to tremble, jitter' and Bewegung 'motion') is the theoretical prediction of a rapid oscillatory motion of elementary particles that obey relativistic wave equations. This prediction was first discussed by Gregory Breit in 1928^[1]^[2] and later by Erwin Schrödinger in 1930^[3]^[4] as a result of analysis of the wave packet solutions of the Dirac equation for relativistic electrons in free space, in which an interference between positive and negative energy states produces an apparent fluctuation (up to the speed of light) of the position of an electron around the median, with an angular frequency of $.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}⁠2mc2/ℏ⁠$ , or approximately 1.6×10²¹ radians per second.

This apparent oscillatory motion is often interpreted as an artifact of using the Dirac equation in a single particle description and disappears when using quantum field theory. For the hydrogen atom, the zitterbewegung is related to the Darwin term, a small correction of the energy level of the s-orbitals.^[5]

^ Breit, Gregory (1928). "An Interpretation of Dirac's Theory of the Electron". Proceedings of the National Academy of Sciences. 14 (7): 553–559. Bibcode:1928PNAS...14..553B. doi:10.1073/pnas.14.7.553. ISSN 0027-8424. PMC 1085609. PMID 16587362.
^ Greiner, Walter (1995). Relativistic Quantum Mechanics. doi:10.1007/978-3-642-88082-7. ISBN 978-3-540-99535-7. S2CID 124404090.
^ Schrödinger, E. (1930). Über die kräftefreie Bewegung in der relativistischen Quantenmechanik [On the free movement in relativistic quantum mechanics] (in German). pp. 418–428. OCLC 881393652.
^ Schrödinger, E. (1931). Zur Quantendynamik des Elektrons [Quantum Dynamics of the Electron] (in German). pp. 63–72.
^ Tong, David (2017). Applications of Quantum Mechanics (PDF). University of Cambridge.

[1] Breit, Gregory (1928). "An Interpretation of Dirac's Theory of the Electron". Proceedings of the National Academy of Sciences. 14 (7): 553–559. Bibcode:1928PNAS...14..553B. doi:10.1073/pnas.14.7.553. ISSN 0027-8424. PMC 1085609. PMID 16587362.

[2] Greiner, Walter (1995). Relativistic Quantum Mechanics. doi:10.1007/978-3-642-88082-7. ISBN 978-3-540-99535-7. S2CID 124404090.

[3] Schrödinger, E. (1930). Über die kräftefreie Bewegung in der relativistischen Quantenmechanik [On the free movement in relativistic quantum mechanics] (in German). pp. 418–428. OCLC 881393652.

[4] Schrödinger, E. (1931). Zur Quantendynamik des Elektrons [Quantum Dynamics of the Electron] (in German). pp. 63–72.

[5] Tong, David (2017). Applications of Quantum Mechanics (PDF). University of Cambridge.

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