Use Equation 3.73 (or Problem 3.18 (c) and (d)) to show that:
(a) For any (normalized) wave packet representing a free particle (V(x)=0), ⟨x⟩ moves at constant velocity (this is the quantum analog to Newton's first law). *Note:* You showed this for a *gaussian* wave packet in Problem 2.42, but it is completely general.
(b) For any (normalized) wave packet representing a particle in the harmonic oscillator potential (V(x)=21mω2x2), ⟨x⟩ oscillates at the classical frequency. *Note:* You showed this for a particular *gaussian* wave packet in Problem 2.49, but it is completely general.