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Equation 1 · Part 2 · Comparing the Main Approaches to Quantum Foundations and Measurement

Symbol a

P(a)=∣⟨a∣ψ⟩∣2P(a) = |\langle a \mid \psi \rangle|^2
aa

What this part means

a is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

a is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

Start with the settled part, because it is smaller than most accounts suggest and it is worth stating precisely. Quantum mechanics gives the Born rule: the probability of a measurement outcome is the squared modulus of a probability amplitude, P(a)=∣⟨a∣ψ⟩∣2P(a) = |\langle a \mid \psi \rangle|^2. for a system in state |ψ\psi⟩\rangle measured in a basis containing |a⟩\rangle . Every interpretation discussed here reproduces this rule for every experiment that has actually been performed. That includes…

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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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