Wave Packet Probability Density Movies

David McIntyre
25 January 2012

Gaussian movie (Fig. 6.9)

wave[k_,x_,t_]:=Exp[I*k*(x-k*t/2)]

gauss[σ_,x_,t_]:=Exp[-(((x-k*t))^2)/4/(σ^2)/(1+I*t/2/(σ^2))]

SetOptions[Plot,Axes->True,AxesLabel->{"x","Re[ψ(x)]"},Ticks->None,PlotStyle->{{Red,AbsoluteThickness[1.5]},{Blue,Dashing[Tiny],AbsoluteThickness[1.5]},{Blue,Dashing[Tiny],AbsoluteThickness[1.5]}},AxesStyle->Directive[FontFamily->"Arial",FontSize->16,Black,AbsoluteThickness[0.5],Arrowheads[0.04]],AspectRatio->1/GoldenRatio,ImageSize->488];

t=120;
k=1;
σ=4;
rng=200;
Plot[{Re[wave[k,x,t]*gauss[σ,x,t]],gauss[σ,x-t]},{x,-rng,rng},PlotRange->{{-25,200},{-1,1.2}},AxesOrigin->{-25,0}]

k=1;
σ=4;
rng=200;
Animate[Plot[{Re[wave[k,x,t]*gauss[σ,x,t]],gauss[σ,x-t]},{x,-rng,rng},PlotRange->{{-25,200},{-1,1.2}},AxesOrigin->{-25,0},PlotPoints->100],{t,0,120},AnimationRunning->False]