Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 15B / a / Solution

The Time-dependent Schrodinger equation is $i\hslash {\partial }_t\psi =\hat{H}\psi$. Differentiate $⟨\hat{A}⟩=⟨\psi |\hat{A}|\psi ⟩$, use the equation and its adjoint, and include explicit time dependence of the operator. This gives Ehrenfest theorem