Initialisierung

h = 6.626068×(10^(-34));
k =1.3806503 (10^(-23));
c =299792458;

α=8π (h/(c^3));
A10[ν_,B10_]=α (ν^3) B10;
B01[B10_]=B10;
u[ν_,T_]=α (ν^3)/(Exp[((h ν)/(k T))]-1);

SetOptions[Plot,FrameLabel->{"Time [ns]","Population"},LabelStyle->{FontFamily->"Helvetica",FontSize->20},Frame->True];

ShowCodeButton:=DynamicModule[{mode=1(*show*)},SelectionMove[EvaluationNotebook[],All,EvaluationCell];
SetOptions[NotebookSelection[EvaluationNotebook[]],CellOpen->False];
Button[Dynamic[If[mode==1,"Show code","Hide code"]],If[mode==1,SelectionMove[EvaluationNotebook[],All,EvaluationCell];
SelectionMove[EvaluationNotebook[],Previous,Cell];SetOptions[NotebookSelection[EvaluationNotebook[]],CellOpen->True];
mode=2,
(*else*)
SelectionMove[EvaluationNotebook[],All,EvaluationCell];
SelectionMove[EvaluationNotebook[],Previous,Cell];SetOptions[NotebookSelection[EvaluationNotebook[]],CellOpen->False];
mode=1
]
]
]

Gleichungen

Planck: u(ν) = α (ν^3)(1/((e^((h ν)/(k T)))-1))

(Subscript[A, 10 ])=  α (ν^3)(Subscript[B, 10])

α = ((8π h)/(c^3))

((d(Subscript[N, 0])(t))/(dt))= (Subscript[N, 1])(t) ((Subscript[A, 10])+(Subscript[B, 10])u(ν))-(Subscript[N, 0])(t) (Subscript[B, 01])u(ν)

((d(Subscript[N, 1])(t))/(dt))= -(Subscript[N, 1])(t) ((Subscript[A, 10])+(Subscript[B, 10])u(ν))+(Subscript[N, 0])(t) (Subscript[B, 01])u(ν)

ShowCodeButton
Manipulate[
timeunit=(10^(-9));sol=NDSolve[{D[N0[t],t]==N1[t] (A10[ν,B10]+B10 u[ν,T])-u [ν,T]B10 N0[t],D[N1[t],t]==-N1[t] (A10[ν,B10]+B10 u[ν,T])+u[ν,T] B10 N0[t],N0[0]==1,N1[0]==0},{N0,N1},{t,0,5timeunit}];
Grid[{{"A10 = "<>ToString[A10[ν,B10],TraditionalForm]},
{"B10 u(ν,T) = "<>ToString[B10 u[ν,T],TraditionalForm]},
{Plot[{Evaluate[N0[t timeunit]/.sol],Evaluate[N1[t timeunit]/.sol]},{t,0,5},PlotRange->{-0.1,1.1},ImageSize->500,Epilog->{Inset[Style["E0",Large,ColorData[1,"ColorList"][[1]],FontFamily->"Helvetica"],Scaled[{0.9,0.9}]],Inset[Style["\n\nE1",Large,ColorData[1,"ColorList"][[2]],FontFamily->"Helvetica"],Scaled[{0.9,0.9}]]}]
}}],{{ν,5 (10.^9),"ν [Hz]"},1,(10^11),ControlType->Slider,Appearance->"Labeled"},{{B10,(10.^35)},0.001,(10^36),ControlType->Slider,Appearance->"Labeled"},{{T,30,"T [K]"},1,300,ControlType->Slider,Appearance->"Labeled"},LabelStyle->Large,SaveDefinitions->True]