Central Forces 2021
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}

If you measured the \(z\)-component of angular momentum, what is the probability that you would measure \(2\hbar\)? \(-3\hbar\)?

If you measured the \(z\)-component of angular momentum, what other possible values could you have obtained with non-zero probability?

if you measured the energy, what possible values could you have obtained with non-zero probability?

What is the probability that the particle can be found in the region \(0<\phi<\frac{\pi}{2}\)?