Measurement Probabilities

  • Quantum Mechanics Spin-1/2 Probability Quantum Measurement
  • Quantum Fundamentals 2022 A beam of spin-\(\frac{1}{2}\) particles is prepared in the initial state \[ \left\vert \psi\right\rangle = \sqrt{\frac{2}{5}}\; |+\rangle_x - \sqrt{\frac{3}{5}}\; |-\rangle_x \](Note: this state is written in the \(S_x\) basis!)
    1. What are the possible results of a measurement of \(S_x\), with what probabilities?
    2. Repeat part a for measurements of \(S_z\).

    3. Suppose you start with a particle in the state given above, measure \(S_x\), and happen to get \(+\hbar /2\). You then take that same particle and measure \(S_z\). What are the possible results and with what probability would you measure each possible result?