Compton-Effekt

Initialisierung

h = 6.626068×(10^(-34));
ℏ=(h/(2π));
k =1.3806503 (10^(-23));
e=1.60217646*(10^(-19));
c =299792458;
me=9.10938215 (10^(-31));
THz=(10^12);GHz=(10^9);MHz=(10^6);
nm=(10^(-9));pm=(10^(-12));

SetOptions[Plot,Frame->True,BaseStyle->{FontFamily->"Helvetica",16}];

Clear[eArrowhead,pArrowhead]

eArrowhead[x_,θ_]:=Min[0.05,0.2 Norm[{{0,0},peprime[νc (10^x),θ/180 π]/pprime[νc (10^x),0][[1]]}]];
pArrowhead[x_,θ_]:=Min[0.05,0.2 Norm[{{0,0},pprime[νc (10^x),θ/180 π]/pprime[νc (10^x),0][[1]]}]];

Plots

Compton-Verschiebung

Δλ[θ_]:=(h/(me c))(1-Cos[θ])
νprime[ν0_,θ_]:=((c ν0)/(c+ν0 (h/(me c))(1-Cos[θ])))
Eeprime[ν0_,θ_]:=h (ν0-νprime[ν0,θ])+me (c^2)
pprime[ν0_,θ_]:=((h νprime[ν0,θ])/c){Cos[θ],Sin[θ]}
peprime[ν0_,θ_]:={h ν0/c,0}-pprime[ν0,θ]
νc=((me (c^2))/h);
λc=(h/(me c));

Manipulate[Show[{Graphics[{Arrowheads[0.05],Arrow[{-pprime[νc (10^x),0],{0,0}}],Gray,Arrowheads[pArrowhead[x,θ]],Arrow[{{0,0},pprime[νc (10^x),θ/180 π]}],Red,Arrowheads[eArrowhead[x,θ]],Arrow[{{0,0},peprime[νc (10^x),θ/180 π]}]},PlotRange->((h νprime[νc (10^x),0])/c)*{{-1,2},{-1,1}},PlotRangeClipping->True],ParametricPlot[{pprime[νc (10^x),θ1/180 π],peprime[νc (10^x),θ1/180 π]},{θ1,0,180},PlotStyle->{{Dashed,Gray},{Dashed,Red}}]}],{{x,0,"ν [(Subscript[ν, c]) (10^x)]"},-5,5,ControlType->Slider,Appearance->"Labeled"},{{θ,90,"θ [°]"},0,180,ControlType->Slider,Appearance->"Labeled"},LabelStyle->20]

Compton-Verschiebung (absolut):

Plot[Δλ[θ/180*π]/λc,{θ,0,180},ImageSize->400,FrameLabel->{"Winkel θ","Δλ [(Subscript[λ, c])]"},PlotStyle->{Thick,Blue},PlotRange->All,FrameTicks->{{Automatic,None},{{0,45,90,135,180},None}}]

Frequenz des ausfallenden Photons

Manipulate[Plot[νprime[νc (10^x),θ/180π+0π/2]/νc,{x,-5,5},ImageSize->400,FrameLabel->{"ν [(Subscript[ν, c]) (10^x)]","ν' [(Subscript[ν, c])]"},PlotStyle->{Thick,Blue},PlotRange->All,Axes->None],{{θ,90},0,180,ControlType->Slider,Appearance->"Labeled"},LabelStyle->20]