English: Gaussian wave function allowed to evolve in free space via the Schrödinger equation

generated with Mathematica using the following lines of code: u[x_, t_, x0_, k0_, om_] :=

Exp[-x0^2*k0^2/2]*
 Exp[-(x - I*x0^2*k0)^2/(2*x0^2*(1 + I*om*t))]/
  Sqrt[x0*Sqrt[Pi]*(1 + I*om*t)]

frame[t_] :=

Plot[Abs[u[x, t, 1, 5, 1]]^2, {x, -5, 35}, Axes -> {True, False}, 
 Ticks -> None, PlotRange -> {0, 1/\[Pi]^(1/4)}]

frames = ParallelTable[frame[t], {t, 0, 5, 0.02}];

Export["constant_momentum_wavefunction_in_free_space.gif", frames]