Central Forces 2021
\(\left|{\Phi}\right\rangle \) is a state for a quantum particle confined to a ring.
\begin{equation}
\left|{\Phi_a}\right\rangle
= i\sqrt\frac{ 2}{12}\left|{3}\right\rangle
- \sqrt\frac{ 1}{12}\left|{1}\right\rangle
+\sqrt\frac{ 3}{12}e^{i\frac{\pi}{4}}\left|{0}\right\rangle
-i\sqrt\frac{ 2}{ 12}\left|{-1}\right\rangle
+\sqrt\frac{ 4}{12}\left|{-3}\right\rangle
\end{equation}
Plot a histogram for the probabilities of \(L_z\).
Make an argument for what you think the expectation value of \(L_z\) will be and mark it with an X on the horizontal-axis of your histogram.