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\centerline{\textbf{Quantum Time Evolution}}
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Two particles are under the influence of an interaction with a Hamiltonian that is proportional to $\hat{S}_{z}$.  At $t=0$, one particle is in the state $\vert + \rangle$ and the other is in the state $\vert + \rangle _{x}$.


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\item What state is each particle in at a later time \textit{t}?

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\item What is the probability that you would measure $S_x = {\hbar \over 2}$ state at time $t$?  Does this probability change with time?


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\item What is the probability that you would measure $S_z = {\hbar \over 2}$ at time $t$?  Does this probability change with time?


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\item Given a Hamiltonian, how would you determine which states are stationary states (states where no probabilities change with time)?  Under what circumstances do measurement probabilities change with time?

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