A Modern Approach to Quantum Mechanics · Problem 6.1

Wave Mechanics in One Dimension — John S. Townsend

Physics — Quantum Mechanics · ehrenfest-theorem-momentum

Problem

Verify that d⟨px⟩dt=iℏ⟨ψ∣[H^,p^x]∣ψ⟩=⟨−dVdx⟩\frac{d\langle p_x\rangle}{dt} = \frac{i}{\hbar}\langle\psi|[\hat{H}, \hat{p}_x]|\psi\rangle = \left\langle -\frac{dV}{dx}\right\rangle for the Hamiltonian H^=p^x2/2m+V(x^)\hat{H} = \hat{p}_x^2/2m + V(\hat{x}).

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