# density operator quantum mechanics

by pere
Tags: density operator, homework question, quantum mechanics
 P: 1 I have the following situation: About the polarization of the photon, I introduce the basis: Horizontal polarization $|\leftrightarrow>=\binom{1}{0}$ Vertical polarization $|\updownarrow>=\binom{0}{1}$ The density matrix in this problem is: $$\rho =\frac{1}{2}\begin{pmatrix} 1+\xi _{1} & \xi_{2}-i\xi _{3}\\ \xi_{2}+i\xi _{3} & 1-\xi _{1} \end{pmatrix}$$ The Stokes parameters are: $\xi _{1}, \xi _{2}, \xi _{3}$ The probability that if the photon has got lineal polarization whose axis forms an angle $\theta$ with de horizontal is: $$|w>=cos\theta |\leftrightarrow>+sin\theta|\updownarrow>$$ $$P_{\theta}==\frac{1}{2}\left ( 1+\xi_{1}cos(2\theta)+\xi_{2}sin(2\theta) \right )$$ Is there any value of the [Stokes parameters](http://en.wikipedia.org/wiki/Stokes_parameters) for which this probability is zero? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution