A particle in a box

Can we make our wave-function look like a particle?

The wave packet as a collection of waves

We start with a wave packet made up of a finite collection of sine waves of the form (e^(i (ϕ-ω t)))Sin[k x].  For a free particle ω=((ℏk)^2)/2m, and to meet the boundry conditions we need (Subscript[k, n])=n π/L.

Ψ[n_,ϕ_]:=Exp[I (ϕ - ω t)] Sin[k x]//.{k->(n+1) π/L,ω->α (k^2)};
SumPsi2=(Ψ[0,0]+Ψ[1,0])/Sqrt[2]/. {α->0.1,L->1};
Manipulate[GraphicsColumn[{Plot[{Re[SumPsi2],Abs[SumPsi2]} /. {t->tNow},{x,0,1},PlotRange->{-1,2},Filling->Bottom],Plot[{Abs[SumPsi2]^2} /. {t->tNow},{x,0,1},PlotRange->{0,2},Filling->Bottom]}],{{tNow,0},0,20/π,0.02,Appearance->"Labeled"}]

Ψ[n_,ϕ_]:=Exp[I (ϕ - ω t)] Sin[k x]//.{k->(n+1) π/L,ω-> α (k^2)};
SumPsi3=(Ψ[1,0]+Ψ[2,0])/Sqrt[2]/. {α->0.1,L->1};
Manipulate[GraphicsColumn[{Plot[{Re[SumPsi3],Abs[SumPsi3]} /. {t->tNow},{x,0,1},PlotRange->{-1,2},Filling->Bottom],Plot[{Abs[SumPsi3]^2} /. {t->tNow},{x,0,1},PlotRange->{0,2},Filling->Bottom]}],{{tNow,0},0,20/π,0.02,Appearance->"Labeled"}]

SumPsi9=(Ψ[0,0]+Ψ[1,ϕ]+Ψ[2,0]+Ψ[3,ϕ]+Ψ[4,0]+Ψ[5,ϕ]+Ψ[6,0]+Ψ[7,ϕ]+Ψ[8,0])/3/. {α->0.1,L->1};
Manipulate[GraphicsColumn[{Plot[{Re[SumPsi9],Abs[SumPsi9]} /. {ϕ->ϕOdd,t->tNow},{x,0,1},PlotRange->{-1,2},Filling->Bottom],Plot[{Abs[SumPsi9]^2} /. {ϕ->ϕOdd,t->tNow},{x,0,1},PlotRange->{0,4},Filling->Bottom]}],{{ϕOdd,0},0,10,0.1,Appearance->"Labeled"},{{tNow,0},0,20/π,0.02,Appearance->"Labeled"}]