A Gaussian wave packet centered around at time with an average initial momentum can be represented by the wavefunction . (For convenience, we take .) The solution of the free-particle Schrödinger equation with this initial condition works out to . The probability density is then given by , where , shown as a black curve. The wave packet remains Gaussian as it spreads out, with its center moving to , thereby following the classical trajectory of the particle. The corresponding momentum probability distribution is given by , shown in red. The rms uncertainties are given by , , which is independent of . This is consistent with the fact that is a constant of the motion for a free particle.