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arXiv · 1008.0924

A unit vector for characterizing the spin polarization of free electron

Chun-Fang Li·Yan Wang
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Abstract

New degrees of freedom having the form of a unit vector are identified for characterizing the spin polarization of free electron. It is shown that when only the spin is considered, the non-commutativity of the Cartesian components of the Pauli vector allows us to use the azimuthal angle of a second direction, denoted by unit vector $\mathbf I$, with respect to the quantization direction to characterize the spin polarization. The rotation of $\mathbf I$ through an angle about the quantization axis leads to a rotation of the spin polarization vector through twice the angle about the same axis. Discussions are also made in Heisenberg picture as well. Upon utilizing this approach to a free electron and letting the quantization direction for each plane wave be the wave vector, we arrive at a representation in which the unit vector $\mathbf I$ functions as an independent index to characterize the spin polarization.

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Chun-Fang Li, Yan Wang. 2010-08-05. A unit vector for characterizing the spin polarization of free electron. https://arxiv.org/abs/1008.0924

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