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## Homework Statement

A spin-half particle is in a known eigenstate of S

_{z}. Show that the product [tex] <S^2_x> < S^2_y> [/tex] is consistent with the Uncertainty principle

## Homework Equations

## The Attempt at a Solution

I know that the generalized uncertainty principle gives [tex] ΔS_x ΔS_y ≥ |<[S_x, S_y]>|

=> ΔS_x ΔS_y ≥ \frac{h^2}{16π^2} [/tex]

but I'm stuck as to how to proceed to show the product in question is consistent with this.

Thanks in advance for any help.