Can I construct |-x> from |+x> in order to find <S_x>?

[cragar]

Homework Statement

|\psi &gt;=a|z&gt;+b|-z&gt;
find &lt;S_x &gt;

The Attempt at a Solution

So I just need to find
&lt;S_x&gt;=({|&lt;x|\psi &gt;|}^2-{|&lt;-x|\psi&gt;|}^2)\frac{\hbar}{2}
right

 

[TSny]

Homework Statement

|\psi &gt;=a|z&gt;+b|-z&gt;
find &lt;S_x &gt;

The Attempt at a Solution

So I just need to find
&lt;S_x&gt;=({|&lt;x|\psi &gt;|}^2-{|&lt;-x|\psi&gt;|}^2)\frac{\hbar}{2}
right

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

 

[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.

 

[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.