construct a Gaussian wavepacket

Please take special note below that I have assigned values for k and omega.  do you undertstand the significance of this?  try changing them

σ  =  5
k  =  2
omega  =  1

    
ψ[x_,  t_]  =  
        Exp[-x^2/(2  σ^2)] 
          Exp[I (k x  -  omega t)];

    
ampf[x_, 
        t_]  =  ψ[x, 
          t] Conjugate[ψ[x, t]]

    
Plot[Re[ψ[x, 1]], {x, -30, 30}, 
      PlotRange -> All]
Plot[ampf[x, 1], {x, -30, 30}, 
      PlotRange -> All]

You can animate the following plots by clicking on the bracket that surrounds them all, then do control-y or animate selected images.  Click the mouse to stop the animation.  You should see the phase evolve in the wavepacket.

Do[
      Plot[Re[ψ[x, t]], {x, -30, 30}, PlotRange -> All], {t, 1, 
        10}]