A Modern Approach to Quantum Mechanics · Problem 6.3

The One-Dimensional Harmonic Oscillator — John S. Townsend

Physics — Quantum Mechanics · translation-operator

Problem

Show for the infinitesimal translation ∣ψ⟩→∣ψ′⟩=T^(δx)∣ψ⟩|\psi\rangle \to |\psi'\rangle = \hat{T}(\delta x)|\psi\rangle that ⟨x⟩→⟨x⟩+δxand⟨px⟩→⟨px⟩.\langle x\rangle \to \langle x\rangle + \delta x \quad \text{and} \quad \langle p_x\rangle \to \langle p_x\rangle.

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