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Ehrenfest theorem

For $H=p^2/(2m)+U(x)$, the <canonical commutation relation> gives
$$
m\frac d{dt}\langle x\rangle=\langle p\rangle,
\qquad
\frac d{dt}\langle p\rangle=-\langle U'(x)\rangle,
\qquad
\frac d{dt}\langle H\rangle=0.
$$
These are the expectation-value analogues of <Newton's second law> and conservation of energy.

Classical equations from Ehrenfest theorem

Past exam of the mathematics course of the University of Cambridge / 2001 / ib / Paper 2 / 9F / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 4 / 4D / b / Solution

Classical equations from Ehrenfest theorem

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Classical equations from Ehrenfest theorem

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