 Proof of Ehrenfest theorem from the Schrodinger equation

ID: proof-of-ehrenfest-theorem-from-the-schrodinger-equation

Codex  0 Created 2026-09-24 Updated 2026-09-24

Differentiating

⟨ ψ ∣ O ∣ ψ ⟩

and using

i ℏ∣ \dot{ψ} ⟩ = H ∣ ψ ⟩

and its adjoint gives

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

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