Quantum Mechanics: Concepts and Applications · Problem 3.24

One-Dimensional Problems — Nouredine Zettili

Physics — Quantum Mechanics · operator-product-time-derivative

Problem

Prove the relation ddt⟨A^B^⟩=⟨∂A^∂tB^⟩+⟨A^∂B^∂t⟩+1iℏ⟨[A^,H^]B^⟩+1iℏ⟨A^[B^,H^]⟩.\frac{d}{dt}\langle \hat{A}\hat{B} \rangle = \left\langle \frac{\partial \hat{A}}{\partial t}\hat{B} \right\rangle + \left\langle \hat{A}\frac{\partial \hat{B}}{\partial t} \right\rangle + \frac{1}{i\hbar}\langle [\hat{A}, \hat{H}]\hat{B} \rangle + \frac{1}{i\hbar}\langle \hat{A}[\hat{B}, \hat{H}] \rangle.

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