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\lhead{Time Dependence for a Quantum Particle on a Ring}
\rhead{\today}
\rfoot{Paradigms in Physics, Oregon State University, Copyright 2020}
\begin{document}
In this activity, your group will carry out calculation on the following quantum state on a ring:
\begin{equation}
|\Phi\rangle=\sqrt{\frac{2}{3}}~|-3\rangle +\frac{1}{\sqrt{6}}~|-1\rangle+\frac{i}{\sqrt{6}}~|3\rangle
\end{equation}
\begin{enumerate}
\item You carry out a measurement to determine the $z$-component of the angular momentum of the particle at time, $t$. Calculate the probability that you measure the $z$-component of the angular momentum to be $3\hbar$. What representation/basis did you use to do this calculation and why did you use this representation?
\item You carry out a measurement to determine the energy of the particle at time, $t$. Calculate the probability that you measure the energy to be $\frac{9\hbar^2}{2I}$. What representation/basis did you use to do this calculation and why did you use this representation?
\item Calculate the probability that the particle can be found in the region $0<\phi<\frac{\pi}{3}$ at some time, $t$. What representation/basis did you use to do this calculation and why did you use this representation?
\item Under what circumstances do measurement probabilities change with time?
\end{enumerate}
\end{document}