How to Calculate Uncertainty for Spin-1/2 Eigenstates?

[nmsurobert]

Homework Statement

Calculate ΔS_x and ΔS_y for an eigenstate S^_z for a spin-1/2 particle. Check to see if the uncertainty relation ΔS_xΔS_y ≥ ħ|<S_z>|/2 is satisfied.

Homework Equations

The Attempt at a Solution

I'm confused on where to start. As I am with most of this quantum stuff.
From what we've done earlier in the class...
ΔS = √(<S²> - <S>²)

and i believe that <S_x²> = ħ²/4 = <S_y²> = <S_z²>

but i don't know where I'm supposed to go from there.

 

[Simon Bridge]

You need to work out <S> now.
Review what is meant by "spin half".

 

[hilbert2]

For this problem, it would be easiest to write the matrix and column vector representations of the spin operators and eigenstates and work with them.
http://easyspin.org/documentation/spinoperators.html