# Homework Help: Quantum Mechanics Spin Expectation Value

1. Oct 31, 2011

### helpcometk

1. The problem statement, all variables and given/known data
What is the expectation valueof the Sχ for a system in the time-dependent state
|Ψ> = 2e-2iωt |z+> -ieiωt |z->

2. Relevant equations
maybe the state must be normalised first i.e 1/√5 times the initial ψ

3. The attempt at a solution
And then say<ψ|Sχ|ψ> where ψ is normalised now and Sx is equal to what ?? .
Maybe Sx =hbar/2 ψ ??? i think in this very last statement i have to be wrong

2. Oct 31, 2011

### dextercioby

Who's z+ and z- ? The normalization factor is ok, provided that z+ and z- are normalized.

3. Oct 31, 2011

### helpcometk

We dont know anything more about z 's ,so this part of problem is solved presumably ,most possibly correct.

4. Oct 31, 2011

### vela

Staff Emeritus
What do you know about the operator Sx?

5. Oct 31, 2011

### helpcometk

Maybe it can take half integer values ? I really dont know anything else.

6. Oct 31, 2011

### vela

Staff Emeritus
Presumably you have a textbook, and it surely covers spin-1/2 systems. Start by reading up on that. Try keeping straight the difference between the operator, its eigenvalues, and its eigenstates. You should be able to calculate what the following equal:
\begin{align*}
\hat{S}_x | \uparrow \rangle = \ ? \\
\hat{S}_x | \downarrow \rangle = \ ?
\end{align*}where the two states are the eigenstates of Sz.

7. Nov 1, 2011

### helpcometk

the only information i managed to found is that Sx |z+> =hbar/2 |z->

and Sx|z->=hbar/2|z+>

but even if we suppose this is correct there is also the problem how to put these in the expression for the expectation value.

8. Nov 1, 2011

### helpcometk

well if this is correct i think i know

9. Nov 1, 2011

### vela

Staff Emeritus
That's correct.

10. Nov 1, 2011

### helpcometk

3q .

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