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IEEJ Transactions on Fundamentals and Materials

Zitterbewegung of Dirac Electron in the point of view of Huang's Expectation Value

Shigeru Sasabe

Published Jan 1, 1999• 0 citations
Publisher

Abstract

The method of Huang's expectation value extracts for a free particle the particulate from the wave function in quantum mechanics. His method is used to investigate the Zitterbewegung of Dirac electron, which disappears in a usual expectation value. Explicit form of the Zitterbewegung as a particle motion is obtained. The uncertainty at the velocity of Dirac electron are examined closely.

DOI
10.1541/ieejfms1990.119.7_952

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The method of Huang's expectation value extracts the particulate behavior of a free particle from its quantum-mechanical wave function. His method is used to investigate the zitterbewegung of the Dirac electron, which disappears in the usual expectation value. An explicit form of the zitterbewegung as a particle motion is obtained. The uncertainty of the velocity of the Dirac electron is examined closely. © 2000 Scripta Technica, Electr Eng Jpn, 132(1): 1–6, 2000

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The method of Huang's expectation value extracts for a free particle the particulate from the wave function in quantum mechanics. His method is used to investigate the Zitterbewegung of Dirac electron, which disappears in a usual expectation value. Explicit form of the Zitterbewegung as a particle motion is obtained. The uncertainty at the velocity of Dirac electron are examined closely.
The detailed motion of a free Dirac electron is investigated by examining the expectation values of the position r and of r×ṙ in a wave packet. It is shown that the well-known zitterbewegung may be looked upon as a circular motion about the direction of the electron spin, with a radius equal to the Compton wavelength (divided by 2π) of the electron. It is further shown that the intrinsic spin of the electron may be looked upon as the “orbital angular momentum” of this motion. The current produced by the zitterbewegung is seen to give rise to the intrinsic magnetic moment of the electron.
The Assessment of the interpretation of Zitterbewegung for free particle solution using various models has been carried out in this work where we firstly considered by using the free particle solution for which Dirac equation and projection operator were carried out.. ln this case, it was invariably revealed that the solution have two doubly degenerate eigenvalues representing positive and negative state that was further support by the analysis which was carried out using Heisenberg’s equation and the representation in relativistic velocity and semi-classical equation of motion for acceleration., but in this second case, the results obtained were observed to have two terms, first terms standing in for rapidly oscillatory motion and the second term representing average motion of the particle in x-direction. The first term in the expression is the one deemed to signify zitterbewegung which is one considered to be sas a result of the fluctuation resulting from the interference between negative and positive energy state while the other term is the normal state terms signifying the average motion of the particle. This therefore confirms the explicit nature of using Dirac equation in handling problems involving the behavior of free particles in field as compared to the use of semiclassical equation of motion.