Consider a system which is given in the following angular momentum eigenstates ∣l,m⟩:
∣ψ⟩=71∣1,−1⟩+A∣1,0⟩+72∣1,1⟩,
where A is a real constant.
(a) Calculate A so that ∣ψ⟩ is normalized.
(b) Calculate the expectation values of L^x, L^y, L^z, and L^2 in the state ∣ψ⟩.
(c) Find the probability associated with a measurement that gives 1ℏ for the z-component of the angular momentum.
(d) Calculate ⟨1,m∣L^+2∣ψ⟩ and ⟨1,m∣L^−2∣ψ⟩.