Quantum Mechanics Spin Expectation Value

[helpcometk]

Homework Statement

What is the expectation valueof the Sχ for a system in the time-dependent state
|Ψ> = 2e^-2iωt |z⁺> -ie^iωt |z->

Homework Equations

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

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

 

[dextercioby]

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

 

[helpcometk]

We don't know anything more about z 's ,so this part of problem is solved presumably ,most possibly correct.

 

[vela]

What do you know about the operator S_x?

 

[helpcometk]

Maybe it can take half integer values ? I really don't know anything else.

 

[vela]

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 S_z.

 

[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.

 

[helpcometk]

well if this is correct i think i know

 

[vela]

That's correct.

 

[helpcometk]

3q .