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Equation 90 · Part 4 · The Atlas That Refuses to Close

Symbol psi

Aw=⟨f∣A^∣ψ⟩⟨f∣ψ⟩,A_w = \frac{\langle f|\hat A|\psi\rangle}{\langle f|\psi\rangle},
ψ\psi

What this part means

psi is an input to the expression that computes the quantity on the left.

Its job in the formula

psi is an input to the expression that computes the quantity on the left.

The passage around this formula

There is a fifth kind of answer to “where,” and it is worth stating precisely how it differs from all four above before using it. Prepare a system in a state |ψ\psi⟩\rangle , couple it weakly to a pointer, and then postselect on a final state |f⟩\rangle measured after the coupling. The weak value of any observable A^\hat A , position among them, conditioned on that postselection is Aw=⟨f∣A^∣ψ⟩⟨f∣ψ⟩A_w = \frac{\langle f|\hat A|\psi\rangle}{\langle f|\psi\rangle}. introduced by Aharonov, Albert, and Vaidman as the quantity a weakly coupled pointer’s mean shift actually reports, to leading order in the coupling strength, once the postselection has been performed [ 11 ] . AwA_w is not an eigenvalue of A^\hat A , not an expectation value in the ordinary sense, and…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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