# Homework Help: Spin expectation value of singlet state from two axes

1. Dec 4, 2012

### bencmier

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

I am just trying to figure out how to start the problem. Any help would be greatly appreciated.

Last edited by a moderator: Apr 17, 2017
2. Dec 4, 2012

### Sourabh N

Start by writing S1 and S2 in terms of the pauli matrices.

3. Dec 4, 2012

### bencmier

Would S1=Sz and S2 have cos(θ) instead of 1's in the matrix?

4. Dec 4, 2012

### Sourabh N

Yes, but you need to be careful about the sign, whether it is cos(θ) or -cos(θ), since the question says -"makes an angle θ down with the z axis".

5. Dec 4, 2012

### bencmier

Ok, but what does the question mean by picking a single basis to work in? I just don't know what the question is saying.

Last edited: Dec 4, 2012
6. Dec 6, 2012

### Sourabh N

I believe they are trying to tell you to have both S_1 and S_2 in the same basis, i.e, either choose S_1 to lie along z-axis and S_2 to lie theta away from it, or choose S_2 to lie along z-axis and S_1 to lie -theta away from it.

Since they already chose the first of these options, the hint is redundant (as the author say so themselves!).

7. Dec 6, 2012

### andrien

may be it will be clear if I show some solution,
Using the notation of question and I use + for up and - for down,

<00|S1S2|00>=-h-/2.h-/2 cosθ.(1/2)(<+-|+->+<-+|-+>),other two terms in brackets which you get are zero because of orthogonality condition.(The extra minus sign in front is just because cos(1800-θ)=-cosθ) and you will get this
=-h-2/4.cosθ(because <+-|+->=1 and similarly for other)
edit:I hope this post will not be deleted like some of my previous ones.

8. Dec 6, 2012

### bencmier

Thank you andrien, your answer was clear and to the point. I don't know why your other posts would have been deleted but this one won't be.

9. Dec 7, 2012

### andrien

it is just because I can not do anyone's homework in this section.I have already gotten infraction for this.But you saw it,so cheers!