Consider a beam of spin-1/2 particles prepared in the quantum state: Answer the following questions. 140)...

 

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Consider a beam of spin-1/2 particles prepared in the quantum state: Answer the following questions. 140) = 1+)-1-). 1. Show that the above state is normalised. Prove that the state is also normalised. |9}2 = e3|+) e|). (2) (3) 2. Using Born's Rule, calculate the probability of measuring S, and getting outcomes +h/2 and -h/2 for both )1 and 2. 3. Comment on your results in Part 2, in particular, on the impact of the overall phase on measurement outcomes. 4. Identify a spatial vector and the associated spin operator S (written as a matrix) for which the state ) is an eigenvector with eigenvalue +/2. Hint: Start by comparing the state ), with the state |+), in your formula sheet. 5. What is the other eigenvector of this same spin operator, with eigenvalue -/2? 6. Calculate the inner product between these two eigenvectors. Consider a beam of spin-1/2 particles prepared in the quantum state: Answer the following questions. 140) = 1+)-1-). 1. Show that the above state is normalised. Prove that the state is also normalised. |9}2 = e3|+) e|). (2) (3) 2. Using Born's Rule, calculate the probability of measuring S, and getting outcomes +h/2 and -h/2 for both )1 and 2. 3. Comment on your results in Part 2, in particular, on the impact of the overall phase on measurement outcomes. 4. Identify a spatial vector and the associated spin operator S (written as a matrix) for which the state ) is an eigenvector with eigenvalue +/2. Hint: Start by comparing the state ), with the state |+), in your formula sheet. 5. What is the other eigenvector of this same spin operator, with eigenvalue -/2? 6. Calculate the inner product between these two eigenvectors.