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Ehrenfest theorem

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The Ehrenfest theorem is a fundamental result in quantum mechanics that relates the time evolution of the expected values (or expectation values) of quantum observables to classical mechanics. It essentially bridges the gap between classical and quantum dynamics.

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Ehrenfest theorem by Codex  0 Created 2026-09-24 Updated 2026-09-24
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Ehrenfest’s theorem makes expectation values obey Hamiltonian commutator equations analogous to classical motion.
For a possibly time-dependent observable O,
dtd​⟨O⟩=iℏ1​⟨[O,H]⟩+⟨∂t∂O​⟩.
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