Angular Momentum Probability

  • Central Forces 2022

    An angular momentum system with \(\ell=1\) is prepared in the state: \begin{equation} |\psi\rangle =\frac{2}{\sqrt{29}}|1,1\rangle+i\frac{3}{\sqrt{29}}|1,0\rangle-\frac{4}{\sqrt{29}}|1,-1\rangle \end{equation}

    1. What are the possible results of a measurement of the angular momentum component \(L_z\), and with what probabilities would they occur?
    2. What are the possible results of a measurement of the angular momentum component \(L_x\), and with what probabilities would they occur? Hint: You may want to use this Spins Reference Sheet or also found here Spins Reference Sheet.
    3. Plot histograms of the predicted measurement results from parts (a) and (b).