A unit vector for characterizing the spin polarization of free electron
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 , with respect to the quantization direction to characterize the spin polarization. The rotation of 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 functions as an independent index to characterize the spin polarization.
Cite
@article{arxiv.1008.0924,
title = {A unit vector for characterizing the spin polarization of free electron},
author = {Chun-Fang Li and Yan Wang},
journal= {arXiv preprint arXiv:1008.0924},
year = {2010}
}
Comments
14 pages with 1 figure. This article was submitted to Phys. Rev. A on May 11, 2010 and was presented as an invited talk in workshop "Spintronics Days" at UPV-EHU (2010), held at Bilbao, Spain during July 27-28, 2010