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Ehrenfest theorem

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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 demonstrates, step-by-step, how to use Ehrenfest theorem to find and solve the equation of motion for a free particle.

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Ehrenfest's theorem

Consider a 1-D free particle, describable as a wave packet at initial 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 <X^2> and <XP + PX>. Integrate these equations.

c) Show that, with a suitable choice of the time origin, the rms deviation <(X-<X>)^2> is given by...

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