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⟨f∣ψ⟩=12(1−i)\langle f|\psi\rangle = \tfrac12(1-i)

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​ 1 ​ ( ∣ ↑ ⟩ + i ∣ ↓ ⟩) . Then ⟨\langle f|ψ\psi⟩\rangle = 12(1−i)\tfrac12(1-i) and ⟨\langle f|σz\sigma_z|ψ\psi⟩\rangle = 12(1+i)\tfrac12(1+i) , so the weak value of σz\sigma_z is

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⟨f∣ψ⟩=12(1−i)\langle f|\psi\rangle = \tfrac12(1-i)

Equation 97 · Evolutionary Physics

The Atlas That Refuses to Close

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

​ 1 ​ ( ∣ ↑ ⟩ + i ∣ ↓ ⟩) . Then ⟨\langle f|ψ\psi⟩\rangle = 12(1−i)\tfrac12(1-i) and ⟨\langle f|σz\sigma_z|ψ\psi⟩\rangle = 12(1+i)\tfrac12(1+i) , so the weak value of σz\sigma_z is

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