Consider a system which is initially in the state
ψ(θ,φ)=51Y1,−1(θ,φ)+53Y10(θ,φ)+51Y11(θ,φ).
(a) Find ⟨ψ∣L^+∣ψ⟩.
(b) If L^z were measured what values will one obtain and with what probabilities?
(c) If after measuring L^z we find lz=−ℏ, calculate the uncertainties ΔLx and ΔLy and their product ΔLxΔLy.