Spreading of a free wave packet:
Consider a free particle
a. Show, applying Enhrenfest's theorem that <X> is a linear function of time, the mean value <P> remaining constant
b. Write the equations of motion for the meal values <X^2> and <XP+PX>. Integrate these equations.
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The solution is attached below in ...
The solution demonstrates, step-by-step, how to use Ehrenfest theorem to find and solve the equation of motion for a free particle.