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:<math> |\psi\rangle \ \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} \psi_x \\ \psi_y \end{pmatrix} = \begin{pmatrix} \cos\theta \exp \left ( i \alpha_x \right ) \\ \sin\theta \exp \left ( i \alpha_y \right ) \end{pmatrix} </math>
is the [[Jones vector]] in the x-y plane. The axes of the ellipse have lengths <math> \sqrt{\tfrac{1 - \sin(2\theta)\cos(\alpha_x - \alpha_y + \pi/2)}{2}}</math> and <math>\sqrt{\tfrac{1 + \sin(2\theta)\cos(\alpha_x - \alpha_y + \pi/2)}{2}}</math>.{{Citation needed|date=November 2008}} If <math>\alpha_x</math> and <math>\alpha_y</math> are equal the wave is [[linear polarization|linearly polarized]]. If they differ by <math>\pi/2\,</math> the wave
==See also==
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