Quantum Fundamentals 2021
Note: The states \(\lvert + \rangle_z\) and \(\lvert - \rangle_z\) are often written without the
subscript \(z\) as \(\lvert + \rangle\) and \(\lvert - \rangle\).
The subscripts are not omitted for the states
\(\lvert + \rangle_x\), \(\lvert - \rangle_x\), \(\lvert + \rangle_y\), and \(\lvert - \rangle_y\).
A beam of spin-\(\frac{1}{2}\) particles is prepared in the state:
\[\left\vert \psi\right\rangle = \frac{2}{\sqrt{13}}\left\vert +\right\rangle+ i\frac{3}{\sqrt{13}} \left\vert -\right\rangle\]
- What are the possible measurement values if you measure the spin component \(S_z\), and with what probabilities would they occur? Check Beasts: Check that you have the right “beast.”
- What are the possible measurement values if you measure the spin component \(S_x\), and with what probabilities would they occur? Check Beasts: Check that you have the right “beast.”
- Use Another Representation: Plot histograms of the predicted measurement results from parts \((a)\) and \((b)\). Your histogram should be a vertical bar chart with the value of the spin component on the horizontal axis and the probability on the vertical axis.