In[]:=
<<Notation`
In[]:=
Symbolize
E
T
;Symbolize
f_
;Symbolize
f_
;
In[]:=
ClearAll["Global`*"]​​$Assumptions={x,t,
E
T
}∈∧{k,
k
0
,ω,ℏ,m,
Δx
0
,Δx,Δp,Δk}∈

>0
;​​
ψ
0
[x_]=
1
4
2π
Δx
0
-
2
x
4
2
Δx
0


k
0
x

;​​f[x_,t_]=
(kx-ω[k]t)

;​​freq=Solve-
2
ℏ
2m
∂
{x,2}
f[x,t]+Vf[x,t]ℏ
∂
t
f[x,t],ω[k][[1,1]];​​

ψ
[k_]=
1
2π
∞
∫
-∞
ψ
0
[x]f[-x,0]x;​​ψ[x_,t_]=
1
2π
∞
∫
-∞

ψ
[k]f[x,t]k/.freq;
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ℏ=1;​​wave:=ParametricPlot3D[{x,Im[ψ[x,t]],Re[ψ[x,t]]},{x,-5,15},PlotRange{{-5,15},{-1,1},{-1,1}},BoxRatios{5,1,1},PlotStyleThickness[.01]];​​amplitude:=ParametricPlot3D[x,Abs[ψ[x,t]]Im[
θ

],Abs[ψ[x,t]]Re[
θ

],{x,-5,15},{θ,-π,π},PlotRange{{-5,15},{-1,1},{-1,1}},BoxRatios{5,1,1},ImageSizeLarge];​​Grid
Grid
"t"
Control[{{t,0},0,3.5,AnimationRunningTrue,AnimationDirectionForwardBackward}]
Dynamic[t]
"
k
0
"
Control[{{
k
0
,5},.1,10,.1}]
Dynamic[
k
0
]
"
Δx
0
"
Control[{{
Δx
0
,1},.1,5,.1}]
Dynamic[
Δx
0
]
"V"
Control{V,0},-10,10,
1
2

Dynamic[V]
"m"
Control[{{m,1},.1,10,.1}]
Dynamic[m]
,AlignmentLeft
DynamicShow{wave,amplitude},PlotLabel"Wave Packet w/ Distortion",AxesLabel{"x","Im(ψ)","Re(ψ)"},ImageSizeAction"Clip",ImageSize{500,200},ViewAngle
π
24
,SphericalRegionFalse,RotationAction"Clip"
SpanFromAbove
DynamicShowwave,ImageSizeAction"Clip",ImageSize{500,200},ViewPointFront,ViewAngle
π
16
,SphericalRegionFalse,RotationAction"Clip"

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