 Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2024/paper-1/a2/b/solution

For a normalized state and a Hermitian quantum observable

\hat{A}

, its quantum uncertainty is the standard deviation of repeated measurement outcomes:

Δ A = ⟨(\hat{A} - ⟨ A ⟩)^{2} ⟩ = ⟨ A^{2} ⟩ - ⟨ A ⟩^{2} .

Here

⟨ A ⟩ = ⟨ Ψ∣ \hat{A} ∣Ψ ⟩

. It is a property of the state and observable, not an instrumental error; the required moments must be finite.

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