Is the Expectation Value of the y-Component of Spin Represented by Sy?

[Sekonda]

Hey,

I'm having trouble interpreting a question, as the solutions say something different... Anyways the question part d) below:

So we want to determine the expectation value of the y-component of the electron spin on the eigenstate of Sx, now I would of thought this was given by:

$$<\uparrow_{x}|\hat{S}_{y}|\uparrow_{x}>$$

However in my solutions it uses the Spin operator in the z-direction instead, I'm note exactly sure what it means by the y-component of the electron spin though I'd of thought this y-component would of been represented by the Spin operator referring to the y components i.e. Sy.

Can someone confirm this? OR tell me why I'm wrong!

Thanks,
SK

 

[vela]

You're right. It's probably just a typo in the solutions.