Equation 97 · The Atlas That Refuses to Close

What does this equation mean?

\langle f|\psi\rangle = \tfrac12(1-i)

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Inputs and operationstfrac12(1-i)

Result or conditionlangle f|psirangle

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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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f

Symbol f

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

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\psi

Symbol psi

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

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i

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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How to interpret it

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What the article says around this equation

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

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Sources cited in the article section

[11] How the Result of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to Be 100 ↗

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