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Using the number-basis matrices for aa and a†a^\dagger (with a∣n⟩=n∣n−1⟩a|n\rangle = \sqrt{n}|n-1\rangle, a†∣n⟩=n+1∣n+1⟩a^\dagger|n\rangle = \sqrt{n+1}|n+1\rangle), evaluate the diagonal element of the commutator [a,a†]=aa†−a†a[a, a^\dagger] = a a^\dagger - a^\dagger a on the state ∣1⟩|1\rangle, i.e. ⟨1∣[a,a†]∣1⟩\langle 1| [a,a^\dagger] |1\rangle.