Suppose for two measurements L and M that [L,M] = 0. Imagine I want to know if the outcome of measurement L is ), and the outcome of measurement M is /j. Noting what we saw about Boolean logic in Lecture 1, can I answer this question? O a. Yes, you always can, quantum mechanics always obeys Boolean logic. O b. Yes, you can, but only because [L,M] = 0, which means L and M commute and Boolean logic works for the given pair of measurables. O c. No, you can't because Boolean logic doesn't work for quantum mechanics, and even if [L,M] = 0 it makes no difference. O d. Pass (I'm not sure and don't want to guess).You'll remember that the spin for an electron can take two possible values 8. = _; (up or down). Noting that S, = $0.Sy = 50, and s, = 50, where Or , y and Or are Pauli matrices, what is the uncertainty relation for As, As, if the spin is in the up state ( u))? O a. ASIAsy 2 : O b. Assy 20 O c. AsAsy > h Od. ASIAsy 2 4 Oe. AsAsy, 2 2h O f. Pass (I'm not sure and don't want to guess).In Question 7 you should have obtained AS, As; 2 4 for the state | u). A fellow student argues that this is connected to the fact that the total spin angular momentum cannot point directly along the z-axis (i.e., the z-component of the spin is smaller than the total spin angular momentum), and as a result the total spin angular momentum vector precesses about the z - aris. Is this argument sensible? O a. True O b. False O c. Pass (I'm not sure and don't want to guess).An interesting thing to realise after doing Question 1 is that ArAp, > ; and AyApy 2 { but A.xAy 2 0 and APApy 2 0. This question has two parts. 1. What is Apro,? Answer this using the multiple choice below. (If you want to do the maths that's ok, but if you think about what it actually is that is underpinning commutation or lack thereof, you probably know the answer without it!) 2. What is the underlying pattern here and how do we determine what are different basis systems in the same Hilbert space and what are not? There is no need to formally answer this one, I just want you to have thought about it before we get to Thursday. O a. Ap:Aor 20 O b. Aprox 2 h O c. APTAOx 2 4 O d. Ap, Aox 2 1 Oe. Ap:Aor 2 2h O f. Pass (I'm not sure and don't want to guess)