Definitions for zitterbewegung
zit·ter·be·we·gung

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1. zitterbewegungnoun

   An extremely fast oscillation of free electrons (and other particles) predicted by some solutions of the Dirac equation

2. Etymology: zittern (to tremble) and Bewegung (motion)

WikipediaRate this definition:0.0 / 0 votes

1. Zitterbewegung

   In physics, the zitterbewegung ("jittery motion" in German, German pronunciation: [ˈtsɪtɐ.bəˌveːɡʊŋ]) is the predicted rapid oscillatory motion of elementary particles that obey relativistic wave equations. The existence of such motion was first discussed by Gregory Breit in 1928 and later by Erwin Schrödinger in 1930 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 what appears to be a fluctuation (up to the speed of light) of the position of an electron around the median, with an angular frequency of 2mc2/ℏ, or approximately 1.6×1021 radians per second. For the hydrogen atom, zitterbewegung can be invoked as a heuristic way to derive the Darwin term, a small correction of the energy level of the s-orbitals.

WikidataRate this definition:1.0 / 1 vote

1. Zitterbewegung

   Zitterbewegung is a theoretical rapid motion of elementary particles, in particular electrons, that obey the Dirac equation. The existence of such motion was first proposed by Erwin Schrödinger in 1930 as a result of his 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 what appears to be a fluctuation of the position of an electron around the median, with a circular frequency of, or approximately 1.6×10^21 Hz. Zitterbewegung also exists in bound-state Dirac solutions. Readers need only to work with Dirac's exact equation second order in time and space to verify this. The large and small components are temporally coupled due to the noncommutation of the gradient and the potential, V, and oscillate in the time with frequency close to the Zitterbewegung frequency. The large and small components can be temporally decoupled either by adiabatic evaluation of the coupling term, which is known as adiabatic elimination in the optical-physics literature on the solution of temporally-coupled equations or by solving the original set of coupled first-order equations using a separation-of-variables solution in which both the large and small components have the same harmonic frequency factor, exp. Both and lead to Dirac's time-independent equation whose analytic eigenvalues and eigenfunctions are given in textbooks. Both and eliminate Zitterbewegung behavior in the bound solutions. Solutions in which Zitterbewegung behavior has not been eliminated are known in an obscure branch of the literature known as 4-space Dirac theory in which the three spatial variables and the scaled time, ct, are treated on an equal footing in order to avoid any suggestion of a preferred frame of reference. In 4-space Dirac theory the positive-energy spectrum is identical to that given by Dirac's time-independent equation in textbooks but the wave function requires a modified interpretation due to contributions from both electrons and positrons. More work is needed to reconcile the 4-space Dirac solution with the conventional Dirac solution accompanied by Dirac's hole interpretation of positron states. All of the above can be more easily understood by recognizing that Dirac's equation has the form of an optical two-level atom in Schroedinger theory, whose energy levels are separated, at least for a free electron, by the Zitterbewegung energy and whose energy levels are coupled coherently. Since differences in 4-space and conventional Dirac solutions would not show up in the spectrum, which provided the original motivation and experimental confirmation of Dirac theory, reconciliation of the two forms of Dirac theory should motivate new experiments to confirm or falsify Zitterbewegung behavior in the 4-space wave functions.

How to pronounce zitterbewegung?

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How to say zitterbewegung in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of zitterbewegung in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of zitterbewegung in Pythagorean Numerology is: 2

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Zitterbewegung
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Zitterbewegung
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=zitterbewegung