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Equation 98 · The Atlas That Refuses to Close

What does this equation mean?

⟨f∣σz∣ψ⟩=12(1+i)\langle f|\sigma_z|\psi\rangle = \tfrac12(1+i)

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operationstfrac12(1+i)
Result or conditionlangle f|sigma_z|psirangle
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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ff

Symbol f

f is part of the quantity the equation computes from the expression on the right.

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σz\sigma_z

Symbol sigma_z

the so the weak value of.

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ψ\psi

Symbol psi

psi is part of the quantity the equation computes from the expression on the right.

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ii

Symbol i

i is one of the signed contributions combined to compute the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

​ 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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Sources cited in the article section

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