Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems A Modern Approach to Quantum Mechanics · Problem 6.6
The One-Dimensional Harmonic Oscillator — John S. Townsend
Physics — Quantum Mechanics · expectation-values-momentum
Problem (a) Show that ⟨ p x ⟩ = 0 \langle p_x\rangle = 0 ⟨ p x ⟩ = 0 ⟨ x ∣ ψ ⟩ \langle x|\psi\rangle ⟨ x ∣ ψ ⟩ ⟨ x ∣ ψ ⟩ \langle x|\psi\rangle ⟨ x ∣ ψ ⟩ ⟨ x ∣ ψ ⟩ → e i p 0 x / ℏ ⟨ x ∣ ψ ⟩ \langle x|\psi\rangle \to e^{ip_0 x/\hbar}\langle x|\psi\rangle ⟨ x ∣ ψ ⟩ → e i p 0 x /ℏ ⟨ x ∣ ψ ⟩ ⟨ x ⟩ → ⟨ x ⟩ and ⟨ p x ⟩ → ⟨ p x ⟩ + p 0 \langle x\rangle \to \langle x\rangle \quad \text{and} \quad \langle p_x\rangle \to \langle p_x\rangle + p_0 ⟨ x ⟩ → ⟨ x ⟩ and ⟨ p x ⟩ → ⟨ p x ⟩ + p 0 Browse the problem library