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:Here $⟨A⟩=⟨\Psi |\hat{A}|\Psi ⟩$. It is a property of the state and observable, not an instrumental error; the required moments must be finite.