density operator quantum mechanics


by pere
Tags: density operator, homework question, quantum mechanics
pere
pere is offline
#1
Jan7-13, 02:26 PM
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:

$$|w>=cos\theta |\leftrightarrow>+sin\theta|\updownarrow>$$

$$ P_{\theta}=<w|\rho|w>=\frac{1}{2}\left ( 1+\xi_{1}cos(2\theta)+\xi_{2}sin(2\theta) \right )$$

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
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