# Homework Help: Finding spin state.

1. Sep 9, 2012

### cragar

1. The problem statement, all variables and given/known data
$|\psi >=a|z>+b|-z>$
find $<S_x >$
3. The attempt at a solution

So I just need to find
$<S_x>=({|<x|\psi >|}^2-{|<-x|\psi>|}^2)\frac{\hbar}{2}$
right

2. Sep 9, 2012

### TSny

Yes, that will get you the answer. If you know the matrix representations of $S_x$, $|z>$, and $|-z>$, then you can also just calculate directly $<S_x>=<\psi |S_x|\psi >$.

3. Sep 9, 2012

### tannerbk

An easy way to do this problem is to write Sx in terms of the raising and lowering operators. The expectation values of both the raising and lowering operators should be obvious.

4. Sep 9, 2012

### cragar

ok thanks for the posts.
If I know what |+x> is. Can I construct |-x> by creating coefficients so that the probability of measuring spin up in the +x and -x equals 1.