# 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+> -ieiωt |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

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

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

What do you know about the operator Sx?

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

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.

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.

well if this is correct i think i know

That's correct.

3q .