Question

4. Spin (10 marks) Suppose an electron is in a state such that its spin can be described by a linear superposition of the eigenspinors of S +A 32 2/22 (a) Normalise the state. (b) What are the possible outcomes of a measurement of the z-component of the spin? What is the probability of each possible result? (c) What are the expectation value and uncertainty of the z-component of the spin? (d) What are the possible results of measuring the x-component of the spin? And what are their associated probabilities? (e) If' we perform a measurement of the r-component of the spin after a measurement of the z- component of the spin, how will the results differ to your answer in (d)?

Answer 1

3 1, -1 2 with.mtt obang(4): 수 , 2 322 3h → Expectation. Value-fs2 2

2 9

The Stete Can he uoritten an a 11 a +b a-b 2. and b: 440) 2

e) If you measure $S_Z$ first it will collapse to one of the eigenstates of the $S_Z$

Then if you measure $S_X$ you will obtain

$\hbar/2$ and $-\hbar/2$ results with equal probabilities, that is the probability will be for both the results.