Two spin-1 particles combine into states with the following angular momenta: s = 2, 1, 0. Use the S-hat− = S-hat1− + S-hat2− operator to write the total angular momentum eigenstate |2,0⟩ in the Sz ⊗ Sz basis. Show that 1/√3 |1,1⟩1 |1,-1⟩2 - 1/√3 |1,0⟩1 |1,0⟩2 + 1/√3 |1,-1⟩1 |1,1⟩2 is a spin-0 eigenstae of the total angular momentum operator.

Two spin-1 particles combine into states with the following angular momenta: s = 2, 1, 0. Use the S-hat− = S-hat1− + S-hat2− operator to write the total angular momentum eigenstate |2,0⟩ in the Sz ⊗ Sz basis. Show that 1/√3 |1,1⟩1 |1,-1⟩2 - 1/√3 |1,0⟩1 |1,0⟩2 + 1/√3 |1,-1⟩1 |1,1⟩2 is a spin-0 eigenstae of the total angular momentum operator.