From standard quantum mechanics we have the known results S b | b + ⟩ ⟩ = ℏ ℏ 2 | b + ⟩ ⟩ and S c | c + ⟩ ⟩ = ℏ ℏ 2 | c + ⟩ ⟩ where | b + ⟩ ⟩ and | c + ⟩ ⟩ are the top spins in their corresponding bases. So we have: ℏ ℏ 2 | c + ⟩ ⟩ = S c | c + ⟩ ⟩ = D ⁡ ⁡ ( y , t ) S b D − − 1 ⁡ ⁡ ( y , t ) | c + ⟩ ⟩ ⇒ ⇒ S b D − − 1 ⁡ ⁡ ( y , t ) | c + ⟩ ⟩ = ℏ ℏ 2 D − − 1 ⁡ ⁡ ( y , t ) | c + ⟩ ⟩