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\centerline{\textbf{Spin One Unknowns}}
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Choose \underline{Unknown \# 1} under the \underline{initialize} menu.  This will cause atoms to leave the oven in a definite quantum state, which we call $\vert \psi_{1} \rangle$.  Now measure the nine probabilities $\left| \langle \phi \vert \psi_{1} \rangle \right| ^{2}$, where $\vert \phi \rangle$ corresponds to spin projections of $\hbar$, $0$, and $-\hbar$ along the three axes.  Fill in the table on the worksheet.  Figure out what $\vert \psi_{1} \rangle$ is.  Repeat for \underline{Unknown \# 4} ($\vert \psi_{4} \rangle$).  In solving for the unknown states, use the convention that the coefficient of $\vert 1 \rangle$ is chosen to be real and positive.  Design an experiment to verify your results.

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\centerline{Unknown $\vert \psi_{1} \rangle$}
\begin{tabular}{|c|c|c|c|} \hline

Probabilities & \multicolumn{3}{c|}{Axis} \\
\hline
Result & x & y & z \\
\hline
$S_{i}=\hbar$ &  &  &  \\
\hline
$S_{i}=0$ &  &  &  \\
\hline
$S_{i}= -\hbar$ &  &  &  \\
\hline
\end{tabular}

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\centerline{Unknown $\vert \psi_{2} \rangle$}
\begin{tabular}{|c|c|c|c|} \hline

Probabilities & \multicolumn{3}{c|}{Axis} \\
\hline
Result & x & y & z \\
\hline
$S_{i}=\hbar$ &  &  &  \\
\hline
$S_{i}=0$ &  &  &  \\
\hline
$S_{i}= -\hbar$ &  &  &  \\
\hline
\end{tabular}

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