Consider a system of total angular momentum j=1. We are interested here in the measurement of J^y; its matrix is given by
J^y=2ℏ0i0−i0i0−i0.
(a) What are the possible values will we obtain when measuring J^y?
(b) Calculate ⟨J^z⟩, ⟨J^z2⟩, and ΔJz if the system is in the state jy=ℏ.
(c) Repeat (b) for ⟨J^x⟩, ⟨J^x2⟩, and ΔJx.