How Is Dispersion in S[x] Computed for the S[z]+ State?

[bjnartowt]

Homework Statement

compute $\left\langle {{{(\Delta {S_x})}^2}} \right\rangle \equiv \left\langle {{S_x}^2} \right\rangle - {\left\langle {{S_x}} \right\rangle ^2}$, where the expectation value is taken for the S[z] +state.

Homework Equations

The Attempt at a Solution

Wait...how can we be speaking of the expectation value for the S[z] state when we are computing the expectation value of the S[x] operator? Is this problem statement saying that the system is in the |+> eigenstate, that is, the state that gives 1/2-hbar from the S[z] operator with 100% certainty? The |+> eigenstate that is a linear combination of the |x;+> and |x;-> eigenstates with a common coefficient of sqrt(2)/2? If so, I sure can evaluate the dispersion in S[x], fo' sho...

 

[fzero]

Yes, they want you to compute $$\langle z;+ | (\Delta S_x)^2|z;+\rangle$$. The rest of your intuition seems on track.