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\centerline{\textbf{Unknown States From a Magnetic Field (Spin-1/2)}}
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Make an unknown state using the following setup with a magnet in between two Stern-Gerlach analyzers:

\centerline{\includegraphics[width=4 in]{spspinhalfbfieldhandfig1.png}}

Consider the magnet for now as a black box that transforms the input $\vert + \rangle_{x}$ state into a new state $\vert \psi \rangle$.  Use \underline{random} as the initial state and set the strength of the magnet to a number from 1-20 corresponding to the position of your computer in the lab.  Use the last analyzer to measure the probabilities for the state $\vert \psi \rangle$ to have six possible spin projections along the three axes.  Keep the first Stern-Gerlach analyzer and the middle magnet oriented as shown in the figure.  Fill in the table on the worksheet and deduce the state $\vert \psi \rangle$, in terms of the $\vert \pm \rangle$ basis.  Design an experiment to verify your results.  From the results of the whole class, can you figure out what the magnet does?

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\centerline{State $\vert \psi \rangle$ made with magnet.  B=\underline{\hspace{50pt}}}
\begin{tabular}{|c|c|c|c|} \hline

Probabilities & \multicolumn{3}{c|}{Axis} \\
\hline
Result & x & y & z \\
\hline
Spin up $\uparrow$ &  &  &  \\
\hline
Spin down $\downarrow $ &  &  &  \\
\hline
\end{tabular}

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