Theorem Problem

Consider a 1-D free particle, describable as a wave packet at inital time t0.

a) Show, applying Ehrenfest's theorem, that (X) is a linear function of time and (P) is a constant.

b) Write the equations of motion for the mean values (X²) and (XP + PX). Integrate these equations.

c) Show that, with a suitable choice of the time origin, the rms deviation ΔX is given by...

Please see attached for full question.