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\lhead{Superposition States 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(\phi)= \sqrt{\frac{8}{5\pi r_0}}\cos^3{(2\phi)}
\end{equation}
\begin{enumerate}
\item If you measured the $z$-component of angular momentum, what is the probability that you would measure $2\hbar$? $-3\hbar$?
\item If you measured the $z$-component of angular momentum, what other possible values could you have obtained with non-zero probability?
\item if you measured the energy, what possible values could you have obtained with non-zero probability?
\item What is the probability that the particle can be found in the region $0<\phi<\frac{\pi}{2}$?
\end{enumerate}
\end{document}