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.

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Question

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 S_z ⊗ S_z 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⟩₂is a spin-0 eigenstae of the total angular momentum operator.

Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.

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Step 2: Calculation of total angular momentum eigen state |2,0> in the state S_z cross S_z basis

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Step 3: proof of spin zero eigen state of total S

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