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Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 2 / 15A / iii / Solution

Differentiating

⟨ O ⟩ = ⟨ ψ ∣ O ∣ ψ ⟩

and using the Schrodinger equation and its adjoint gives the Ehrenfest theorem

\frac{d}{d t} ⟨ O ⟩ = \frac{1}{i ℏ} ⟨[O, H]⟩ + ⟨ \frac{\partial O}{\partial t} ⟩ .

Solved by gpt-5.6-sol high.

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