Question

Prove the relation\\ $\frac{d}{dt} \langle \hat{A}\hat{B} \rangle = \langle \frac{\partial \hat{A}}{\partial t} \hat{B} \rangle + \langle \hat{A}\frac{\partial \hat{B}}{\partial t} \rangle + \frac{1}{i\hbar} \langle [\hat{A}, \hat{H}]\hat{B} \rangle + \frac{1}{i\hbar} \langle \hat{A}[\hat{B}, \hat{H}] \rangle$

          Prove the relation\\
$\frac{d}{dt} \langle \hat{A}\hat{B} \rangle = \langle \frac{\partial \hat{A}}{\partial t} \hat{B} \rangle + \langle \hat{A}\frac{\partial \hat{B}}{\partial t} \rangle + \frac{1}{i\hbar} \langle [\hat{A}, \hat{H}]\hat{B} \rangle + \frac{1}{i\hbar} \langle \hat{A}[\hat{B}, \hat{H}] \rangle$

Prove the relation

(d)/(dt)⟨ÂB̂⟩ = ⟨(∂Â)/(∂ t)B̂⟩ + ⟨Â(∂B̂)/(∂ t)⟩ + (1)/(iħ)⟨ [Â, Ĥ]B̂⟩ + (1)/(iħ)⟨Â[B̂, Ĥ] ⟩

Added by Encarnacion F.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Urvashi Arora

07/24/2021

Step 1

Step 1: Start with the left-hand side of the equation: (d/dt)(:hat(A)hat(B):) Show more…

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Prove the relation (d)/(dt)(:hat(A)hat(B):)=(:(del(hat(A)))/(delt)(hat(B)):)+(:(hat(A))(del(hat(B)))/(delt):)+(1)/(iℏ)(:[hat(A),hat(H)]hat(B):)+(1)/(iℏ)(:hat(A)[hat(B),hat(H)]:) Prove the relation A,H]B}+ (A[B,H]) ih ih