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\lhead{Expectation Values for a Particle on a Ring}
\rhead{\today}
\rfoot{Paradigms in Physics, Oregon State University, Copyright 2020}


\begin{document}
Consider the following normalized abstract 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 What is the expectation value of $\hat{L}_z$ as a function of time for this state?
\item What is the expectation value of the energy as a function of time for this state? 
\end{enumerate}

\end{document}
