Superposition States for a Particle on a Ring

  • 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}
    1. If you measured the \(z\)-component of angular momentum, what is the probability that you would measure \(2\hbar\)? \(-3\hbar\)?
    2. If you measured the \(z\)-component of angular momentum, what other possible values could you have obtained with non-zero probability?
    3. if you measured the energy, what possible values could you have obtained with non-zero probability?
    4. What is the probability that the particle can be found in the region \(0<\phi<\frac{\pi}{2}\)?