- #1

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## Homework Statement

A beam of neutrons (moving along the z-direction) consists of an incoherent superposition of two beams that were initially all polarized along the x- and y-direction, respectively.

Using the Pauli spin matrices:

[tex]

\sigma_x = \begin{pmatrix}

0 & 1 \\

1 & 0 \\

\end{pmatrix},

\sigma_y = \begin{pmatrix}

0 & -i \\

i & 0 \\

\end{pmatrix},

\sigma_z = \begin{pmatrix}

1 & 0 \\

0 & -1 \\

\end{pmatrix}

[/tex]

give the density matrix ## \hat{\rho} ## for this beam and determine the mean polarization ## \langle\vec{\sigma}\rangle = tr \hat{\rho}\vec{\sigma}##

2. Homework Equations

2. Homework Equations

## \hat{\rho} = \sum_n c_n |n\rangle \langle n |## Where ##c_n## is the relative probability to be in state n. Spin states ##|+\rangle = |1/2,1/2\rangle, |-\rangle = |1/2,-1/2\rangle ##

## The Attempt at a Solution

I'm not sure what it means that the beams were initially polarized along the x- and y-axis and I don't know where to start with this problem.

I'm guessing with polarization they mean the direction of the spin?

Does the polarization change with time since they explicitly mention that it's the initial state?