s[s0_,delta_,Gam_]:=s0/(1+(2delta/Gam)^2);
w[s0_,delta_,Gam_]:=1/(1+s[s0,delta,Gam]);
Omega[s0_,delta_,Gam_]:=Sqrt[2s0(delta^2+Gam^2/4)/(1+(2delta/Gam)^2)];
rhoeg[s0_,delta_,Gam_]:=I Omega[s0,delta,Gam]/(2(Gam/2-I delta)(1+s[s0,delta,Gam]));
Bu[s0_,delta_,Gam_]:=2Re[rhoeg[s0,delta,Gam]];
Bv[s0_,delta_,Gam_]:=2Im[rhoeg[s0,delta,Gam]];
Bw[s0_,delta_,Gam_]:=-w[s0,delta,Gam];

Rfx[s0_,delta_,Gam_]:=Omega[s0,delta,Gam];
Rfy[s0_,delta_,Gam_]:=0;
Rfz[s0_,delta_,Gam_]:=delta;

NormRf[s0_,delta_,Gam_]:=Sqrt[Rfx[s0,delta,Gam]^2+Rfy[s0,delta,Gam]^2+Rfz[s0,delta,Gam]^2];

Aquator[phi_]:={Sin[phi],Cos[phi],0};
Meridian0[phi_]:={Sin[phi],0,Cos[phi]};
MeridianPi[phi_]:={0,Sin[phi],Cos[phi]};


BlochVector[s0_,delta_,Gam_]:={Bu[s0,delta,Gam],Bv[s0,delta,Gam],Bw[s0,delta,Gam]};
FieldVectorNormalized[s0_,delta_,Gam_]:={Rfx[s0,delta,Gam],Rfy[s0,delta,Gam],Rfz[s0,delta,Gam]}/NormRf[s0,delta,Gam];
FieldVector[s0_,delta_,Gam_]:=1.2*{Rfx[s0,delta,Gam],Rfy[s0,delta,Gam],Rfz[s0,delta,Gam]}/Rfx[s0,delta,Gam];
Gamma0=1;
s00=1;
Animate[Show[ParametricPlot3D[{Aquator[phi],Meridian0[phi],MeridianPi[phi]},{phi,0,2Pi },PlotStyle->{{Black,Dashing[0.01],Thickness[0.001]}},PlotRange->{{-1.5,1.5},{-1.5,1.5},{-1.5,1.5}},Axes->None,Boxed->False],ParametricPlot3D[{BlochVector[s00,delta,Gamma0],FieldVectorNormalized[s00,delta,Gamma0]},{delta,-10,10 },PlotStyle->{{"DarkCyan",Thickness[0.008]},{"Coral",Thickness[0.008]}},PlotRange->{{-1.5,1.5},{-1.5,1.5},{-1.5,1.5}},Axes->None,Boxed->True],Graphics3D[{Text["|e>",{0,0,1.1}],Text["|g>",{0,0,-1.1}],Thickness[0.01],Opacity[0.2],Sphere[{0,0,0},1],Blue,Opacity[1],Arrow[Tube[{{0,0,0},BlochVector[s00,delta2,Gamma0]},0.015]],Red,Arrow[Tube[{{0,0,0},0.5*FieldVector[s00,delta2,Gamma0]},0.015]]}]],{delta2,-10,10},{s00,0,10},AnimationRunning->False]

Plot[Sin[x],{x,0,40},Axes->None, AspectRatio-> 0.2,PlotStyle->{Red,Thickness[0.015]}]

Plot[Sin[x],{x,0,2Pi},Axes->None, AspectRatio-> 0.6,PlotStyle->{Black,Thickness[0.01]}]

Plot[Exp[-t],{t,0,3},PlotRange->{{0,3}{0,1}} AspectRatio-> 0.4,PlotStyle->{Red,Thickness[0.005]},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Bold,Large]]

Plot[Exp[-t^2],{t,-3,3},PlotRange->{{-3,3},{0,1.2}} ,PlotStyle->{Red,Thickness[0.005]},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Bold,Small,White]]

Plot[x,{x,-3,3},PlotRange->{{-3,3},{-3,3}} ,AspectRatio->0.9,PlotStyle->{Red,Thickness[0.005]},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Bold,Small,White]]

Plot[Exp[-t^2]t,{t,-3,3},PlotRange->{{-3,3},{-0.5,0.5}} ,AspectRatio->0.9,PlotStyle->{Red,Thickness[0.005]},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Bold,Small,White]]

(* Rabi oscillations *)

Pe[t_,Om_,delta_]:=((Om)/(Sqrt[Om^2+delta^2]) Sin[Sqrt[Om^2+delta^2] t/2]  )^2
Plot[{Pe[t,1,0]},{t,0,10},PlotRange->{{0,10}{0,1}} AspectRatio-> 0.4,PlotStyle->{{Red,Thickness[0.005]},{Blue,Thickness[0.005]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Pe[t_,Om_,delta_]:=((Om)/(Sqrt[Om^2+delta^2]) Sin[Sqrt[Om^2+delta^2] t/2]  )^2
Plot[{Pe[t,1,0],Pe[t,1,1]},{t,0,10},PlotRange->{{0,10}{0,1}} AspectRatio-> 0.4,PlotStyle->{{Red,Thickness[0.005]},{Blue,Thickness[0.005]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Pe[t_,Om_,delta_]:=((Om)/(Sqrt[Om^2+delta^2]) Sin[Sqrt[Om^2+delta^2] t/2]  )^2
Plot[{Pe[t,1,0],Pe[t,1,1],Pe[t,1,2.5]},{t,0,10},PlotRange->{{0,10}{0,1}} AspectRatio-> 0.4,PlotStyle->{{Red,Thickness[0.005]},{Blue,Thickness[0.005]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Pe[t_,Om_,delta_]:=((Om)/(Sqrt[Om^2+delta^2]) Sin[Sqrt[Om^2+delta^2] t/2]  )^2
Plot[{Pe[Pi,1,d]},{d,-6,6},PlotRange->{{-6,6},{0,1.05}} ,AspectRatio-> 0.6,PlotStyle->{{Red,Thickness[0.005]},{Blue,Thickness[0.005]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

(* light shifts in dressed state picture *)
Eg[Om_,delta_]:=0.5*(-delta+Sqrt[Om^2+delta^2]);
Ee[Om_,delta_]:=0.5*(-delta-Sqrt[Om^2+delta^2]);
Plot[{Eg[Om,-1],Ee[Om,-1]},{Om,0,5},PlotRange->{{0,4},{-2,3}} ,AspectRatio-> 0.8,PlotStyle->{{Red,Thickness[0.005]},{Blue,Thickness[0.005]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]
Plot[{Ee[Om,1],Eg[Om,1]},{Om,0,5},PlotRange->{{0,4},{-3,2}} ,AspectRatio-> 0.8,PlotStyle->{{Red,Thickness[0.005]},{Blue,Thickness[0.005]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

(* light shifts *)
Clear["Global`*"]
Eg0=0;
Ee0=3;
Eg[Om_,delta_]:=Eg0+0.5*(-delta+Sign[delta]Sqrt[Om^2+delta^2]);
Ee[Om_,delta_]:=Ee0+delta+0.5*(-delta-Sign[delta]Sqrt[Om^2+delta^2]);

Plot[{Eg[Om,-1],Ee[Om,-1]},{Om,0,4},PlotRange->{{0,4},{-2,5}} ,AspectRatio-> 0.8,PlotStyle->{{Blue,Thickness[0.01]},{Red,Thickness[0.01]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Eg0=0;
Ee0=0.2;
Eg[Om_,delta_]:=Eg0+0.5*(-delta+Sign[delta]Sqrt[Om^2+delta^2]);
Ee[Om_,delta_]:=Ee0+delta+0.5*(-delta-Sign[delta]Sqrt[Om^2+delta^2]);
Plot[{Eg[Om,-1],Ee[Om,-1]},{Om,0,0.5},PlotRange->{{0,0.5},{-0.1,0.3}} ,AspectRatio-> 0.8,PlotStyle->{{Blue,Thickness[0.01]},{Red,Thickness[0.01]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]
Plot[{Eg[Om,1],Ee[Om,1]},{Om,0,0.5},PlotRange->{{0,0.5},{-0.1,0.3}} ,AspectRatio-> 0.8,PlotStyle->{{Blue,Thickness[0.01]},{Red,Thickness[0.01]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Eg0=0;
Ee0=0.2;
Eg[Om_,delta_]:=Eg0+0.1delta Om;
Ee[Om_,delta_]:=Ee0-0.1delta Om;
Plot[{Eg[Om,-1],Ee[Om,-1]},{Om,0,0.5},PlotRange->{{0,0.5},{-0.1,0.3}} ,AspectRatio-> 0.8,PlotStyle->{{Blue,Thickness[0.01]},{Red,Thickness[0.01]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},AxesLabel->None,TicksStyle->Directive[FontOpacity->0,FontSize->0]]
Plot[{Eg[Om,1],Ee[Om,1]},{Om,0,0.5},PlotRange->{{0,0.5},{-0.1,0.3}} ,AspectRatio-> 0.8,PlotStyle->{{Blue,Thickness[0.01]},{Red,Thickness[0.01]},{Green,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},AxesLabel->None,TicksStyle->Directive[FontOpacity->0,FontSize->0]]

Eg0=0;
Ee0=0;
Eg[Om_,delta_]:=Eg0+0.5*(-delta+Sign[delta]Sqrt[Om^2+delta^2]);
Ee[Om_,delta_]:=Ee0+delta+0.5*(-delta-Sign[delta]Sqrt[Om^2+delta^2]);


Egd[Om_,delta_]:=Eg[Om,delta]-Eg[0,delta]+delta;
Eed[Om_,delta_]:=Ee[Om,delta]-Eg[0,delta];

Egdu[Om_,delta_]:=Eg[0,delta]-Eg[0,delta]+delta;
Eedu[Om_,delta_]:=Ee[0,delta]-Eg[0,delta];

Egs[Om_,delta_]:=If[delta<0,Egd[Om,delta],Eed[Om,delta]];
Ees[Om_,delta_]:=If[delta<0,Eed[Om,delta],Egd[Om,delta]];

GroundStateProbability[Om_,delta_]:=(Normalize[Eigenvectors[(({{-delta, Om}, {Om, delta}}))][[1]]][[1]])^2;
ExcitedStateProbability[Om_,delta_]:=1-GroundStateProbability[Om,delta];

Plotg=Plot[Egs[1,delta],{delta,-3,3},PlotRange->{{-3.4,3.4},{-3.4,3.4}},AspectRatio-> 0.8,ColorFunctionScaling->False,ColorFunction->Function[{delta},Blend[ColorConvert[{Blue,Red},"RGB"],GroundStateProbability[1,delta]]],PlotStyle->{Thickness[0.01]},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large],AxesOrigin->{-3,-3}];

Plote=Plot[Ees[1,delta],{delta,-3,3},PlotRange->{{-3.4,3.4},{-3.4,3.4}},AspectRatio-> 0.8,ColorFunctionScaling->False,ColorFunction->Function[{delta},Blend[ColorConvert[{Blue,Red},"RGB"],ExcitedStateProbability[1,delta]]],PlotStyle->{Thickness[0.01]},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large],AxesOrigin->{-3,-3}];

Plotb=Plot[{Egdu[1,delta],Eedu[1,delta]},{delta,-3,3} ,PlotRange->{{-3.4,3.4},{-3.4,3.4}},AspectRatio-> 0.8,PlotStyle->{{Blue,Dashed,Thickness[0.005]},{Red,Dashed,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large],AxesOrigin->{-3,-3}]

Show[Plotg,Plote,Plotb]

ScattRate[s0_,delta_,gamma_]:=(s0  gamma 0.5 /(1+s0+(2 delta/gamma)^2))/gamma; (* in units of gamma *)

Plot[{ScattRate[0.1,delta,1],ScattRate[1,delta,1],ScattRate[10,delta,1],ScattRate[100,delta,1]},{delta,-10,10} ,PlotRange->{{-10,10},{0,0.5}},AspectRatio-> 0.6,PlotStyle->{{Green,Thickness[0.005]},{Blue,Thickness[0.005]},{Magenta,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large],AxesOrigin->{-10,0},Ticks->{{-10,-5,0,5,10},{0,0.1,0.2,0.3,0.4,0.5}}]

PhaseShift[s0_,delta_,gamma_]:=Arg[I/((gamma/2-I delta)(1+(s0/(1+(2 delta / gamma)^2))))]; 

Plot[ScattRate[1,delta,1],{delta,-4,4} ,PlotRange->{{-4,4},{0,0.275}},AspectRatio-> 0.4,PlotStyle->{{Red,Thickness[0.01]},{Red,Thickness[0.01]},{Blue,Dashed,Thickness[0.005]},{Red,Dashed,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large],AxesOrigin->{-4,0},Ticks->{{},{0,0.1,0.2}}]

Plot[PhaseShift[1,delta,1],{delta,-4,4} ,PlotRange->{{-4,4},{0 ,Pi}},AspectRatio-> 0.4,PlotStyle->{{Red,Thickness[0.01]},{Red,Thickness[0.01]},{Blue,Dashed,Thickness[0.005]},{Red,Dashed,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large],AxesOrigin->{-4,0},Ticks->{{-4,-2,0,2,4},{0,Pi/2,Pi}}]

Lambda=780*10^-9;
k=2Pi/Lambda;
s0=0.1;
Gam=6*10^6;
s[sign_,v_,delta_,s0_]:= s0/(1+4(delta+sign k v)^2/Gam^2);
F[v_,delta_,s0_]:= (s[-1,v,delta,s0]-s[1,v,delta,s0]) ;
FNorm[v_,delta_,s0_]:=F[v,delta,s0]/s[-1,0,0,s0];
FPlus[v_,delta_,s0_]:=s[-1,v,delta,s0]/s[-1,0,0,s0];
FMinus[v_,delta_,s0_]:=-s[1,v,delta,s0]/s[-1,0,0,s0];

delta=-0.1Gam/2;



Plot[{FNorm[v*Gam/k,delta,s0],FPlus[v*Gam/k,delta,s0],FMinus[v*Gam/k,delta,s0]},{v,-3,3} ,AspectRatio-> 0.4,PlotRange->All,PlotStyle->{{Magenta,Thickness[0.005]},{Blue,Dashed,Thickness[0.005]},{Red,Dashed,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

delta=-1Gam/2;



Plot[{FNorm[v*Gam/k,delta,s0],FPlus[v*Gam/k,delta,s0],FMinus[v*Gam/k,delta,s0]},{v,-3,3} ,AspectRatio-> 0.4,PlotRange->All,PlotStyle->{{Magenta,Thickness[0.005]},{Blue,Dashed,Thickness[0.005]},{Red,Dashed,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

delta=-3Gam/2;



Plot[{FNorm[v*Gam/k,delta,s0],FPlus[v*Gam/k,delta,s0],FMinus[v*Gam/k,delta,s0]},{v,-3,3} ,AspectRatio-> 0.4,PlotRange->All,PlotStyle->{{Magenta,Thickness[0.005]},{Blue,Dashed,Thickness[0.005]},{Red,Dashed,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

delta=-1Gam/2;
spacing=4;
Plot[{FNorm[v*Gam/k,delta,s0]+FNorm[v*Gam/k,spacing delta,s0],FPlus[v*Gam/k,delta,s0],FPlus[v*Gam/k,spacing delta,s0],FMinus[v*Gam/k,delta,s0],FMinus[v*Gam/k,spacing delta,s0]},{v,-3,3} ,AspectRatio-> 0.4,PlotRange->All,PlotStyle->{{Magenta,Thickness[0.005]},{Blue,Dashed,Thickness[0.005]},{Blue,Dashed,Thickness[0.005]},{Red,Dashed,Thickness[0.005]},{Red,Dashed,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Clear["Global`*"]
Lambda=780*10^-9;
k=2Pi/Lambda;
s0=0.1;
Gam=6*10^6;
s[sign_,v_,delta_,s0_]:= s0/(1+4(delta+sign k v)^2/Gam^2);
F[v_,delta_,s0_]:= s[1,v,delta,s0]/(1+s[1,v,delta,s0]);
FNorm[v_,delta_,s0_]:=F[v,delta,s0]/s[-1,0,0,s0];


delta=-Gam/2;



Plot[{FNorm[v*Gam/k,delta,s0]},{v,-3,3} ,AspectRatio-> 0.4,PlotRange->All,PlotStyle->{{Magenta,Thickness[0.005]},{Blue,Dashed,Thickness[0.005]},{Red,Dashed,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

data1=RandomFunction[RandomWalkProcess[.5],{0,100}];
data2=RandomFunction[RandomWalkProcess[.5],{0,100}];
data3=RandomFunction[RandomWalkProcess[.5],{0,100}];
data4=RandomFunction[RandomWalkProcess[.5],{0,100}];
data5=RandomFunction[RandomWalkProcess[.5],{0,100}];
data6=RandomFunction[RandomWalkProcess[.5],{0,100}];
data7=RandomFunction[RandomWalkProcess[.5],{0,100}];
data8=RandomFunction[RandomWalkProcess[.5],{0,100}];
data9=RandomFunction[RandomWalkProcess[.5],{0,100}];
data10=RandomFunction[RandomWalkProcess[.5],{0,100}];
ListPlot[{data1,data2,data3,data4,data5,data6,data7,data8,data9,data10},Joined->True]

Tilt=0.000;
NrWalks=10;
Leng=2000;
data1=Table[0,{NrWalks},{Leng},{2}];
For[WalkNr=1,WalkNr<NrWalks,WalkNr++,
data1[[WalkNr,1,1]]=1;
For[i=2,i<Leng+1,i++,
data1[[WalkNr,i,1]]=i;
rand=Random[]*2-1-Tilt*data1[[WalkNr,i-1,2]];
(*rand=RandomInteger[]*2-1;*)
If[rand>0,step=1,step=-1];
data1[[WalkNr,i,2]]=data1[[WalkNr,i-1,2]]+step;
]
]
ListPlot[data1,Joined->True,PlotRange->{{0,Leng},{-100,100}},AspectRatio->0.4]

Tilt=0.010;
NrWalks=10;
Leng=2000;
data1=Table[0,{NrWalks},{Leng},{2}];
For[WalkNr=1,WalkNr<NrWalks,WalkNr++,
data1[[WalkNr,1,1]]=1;
For[i=2,i<Leng+1,i++,
data1[[WalkNr,i,1]]=i;
rand=Random[]*2-1-Tilt*data1[[WalkNr,i-1,2]];
(*rand=RandomInteger[]*2-1;*)
If[rand>0,step=1,step=-1];
data1[[WalkNr,i,2]]=data1[[WalkNr,i-1,2]]+step;
]
]
ListPlot[data1,Joined->True,PlotRange->{{0,Leng},{-100,100}},AspectRatio->0.4]

Plot[{Sin[ 2Pi 2t+Pi/4]/2-0.5,-Sin[2Pi 2 t+Pi/4]/2-0.5},{t,0,1} ,AspectRatio-> 0.3,PlotStyle->{{Red,Thickness[0.005]},{Blue,Thickness[0.005]},{Magenta,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Plot[{Sin[ 2Pi 2t+Pi/4]/2-0.5,-Sin[2Pi 2 t+Pi/4]/2-0.5},{t,0,1} ,AspectRatio-> 0.3,PlotStyle->{{Red,Thickness[0.005]},{Blue,Thickness[0.005]},{Magenta,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large],Axes->None]

Clear["Global`*"]
kB=1.3806503*10^-23;
a0=0.052917721086*10^-9;
hbar=1.05457148*10^-34;
h=2*Pi*hbar;
massunit=1.66053886*10^-27;
T=600+300;
m=84*massunit;
P[v_,T_,m_]:=(m/ (kB T))^2 v^3 Exp[-m v^2/(2 kB T)]/2;
Plot[{P[v,273+600,84*massunit],P[v,273+150,87*massunit]},{v,0,1500} ,AspectRatio-> 0.3,PlotStyle->{{Blue,Thickness[0.005]},{Red,Thickness[0.005]},{Magenta,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Clear["Global`*"]
P[v_,T_,m_]:=(m/ (kB T))^2 v^3 Exp[-m v^2/(2 kB T)]/2;
Integrate[(m/ (kB T))^2 v^3 Exp[-m v^2/(2 kB T)]/2,{v,0,Infinity}]

Clear["Global`*"]
kB=1.3806503*10^-23;
a0=0.052917721086*10^-9;
hbar=1.05457148*10^-34;
h=2*Pi*hbar;
massunit=1.66053886*10^-27;
T=600+300;
muB=9.27400968*10^-24;
m=84*massunit;
Lambda=780*10^-9;
k=2Pi/Lambda;
a=50000;
v0=300;
Boffset=-100*10^-4;
z0=v0^2/(2a);
B0=hbar k v0/muB;
Plot[10000(Boffset+B0 Sqrt[1-z/z0]),{z,0,z0} ,PlotRange->{{0,z0},{-100,200}},AspectRatio-> 0.3,PlotStyle->{{Red,Thickness[0.005]},{Blue,Thickness[0.005]},{Magenta,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Plot[{v0^2/(10^6),v0^2/(2*50000)},{v0,0,1000} ,AspectRatio-> 0.6,PlotStyle->{{Blue,Thickness[0.005]},{Red,Thickness[0.005]},{Magenta,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Clear["Global`*"]
Lambda=10^-9;
z0[w0_]:=N[Pi*w0^2/Lambda];
w[z_,w0_]:=w0*(1+(z/z0[w0])^2)^0.5;
GaussStrahl[x_,y_,z_,w0_]:=(w[0,w0]^2/(w[z,w0]^2))Exp[-x^2/w[z,w0]^2]Exp[-y^2/w[z,w0]^2]
Waist0=10*10^-9;
ContourPlot3D[GaussStrahl[x*10^-9,y*10^-9,z*10^-9,Waist0]==0.9,{x,-2*Waist0*10^9,2*Waist0*10^9},{y,-2*Waist0*10^9,2*Waist0*10^9},{z,-10*Waist0*10^9,10*Waist0*10^9}]

Plot3D[-GaussStrahl[x*10^-9,0*10^-9,z*10^-9,Waist0],{x,-2*Waist0*10^9,2*Waist0*10^9},{z,-30*Waist0*10^9,30*Waist0*10^9}]

Plot[{-10*Exp[-x^2]-x,-x},{x,-3,3},PlotRange->{{-3,3},{-10.5,3.1}},Axes->None, AspectRatio-> 2,PlotStyle->{{Black,Thickness[0.015]},{Black,Dashed,Thickness[0.005]}}]

PlotRb=LogLogPlot[{10^10 Exp[2 Log[N]]},{N,10^5,10^8} , PlotRange->All,AspectRatio-> 1, GridLines->Automatic,
PlotStyle->{{Red,Thickness[0.01]},{Blue,Thickness[0.005]},{Magenta,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

PlotSr=LogLogPlot[{ 10^23 Exp[-3 Log[N]]},{N,3 10^7,10^8} , PlotRange->All,AspectRatio-> 1, GridLines->Automatic,
PlotStyle->{{Blue,Thickness[0.01]},{Blue,Thickness[0.005]},{Magenta,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Show[PlotRb,PlotSr]

LogLogPlot[{2.6 10^13 Exp[-2 Log[N]]},{N,10^7,10^8} ,AspectRatio-> 1, GridLines->Automatic,
PlotStyle->{{Red,Thickness[0.01]},{Blue,Thickness[0.005]},{Magenta,Thickness[0.005]},{Red,Thickness[0.005]}},FrameLabel->{time, probability},AxesStyle->{Directive[Thick],Directive[Thick]},TicksStyle->Directive[Thick],LabelStyle->Directive[Large]]

Plot[x^2,{x,-40,40},Axes->None, AspectRatio-> 1,PlotStyle->{Red,Thickness[0.005]}]

Plot[{Sqrt[k^2+k^4],k^2},{k,0,2},Axes->None, AspectRatio-> 0.5,PlotStyle->{Red,Thickness[0.005]}]

Plot[Exp[-x^2],{x,-3,3},Axes->None, AspectRatio-> 0.3,PlotStyle->{Red,Thickness[0.005]}]

Plot[Sin[x],{x,0,80},Axes->None,PlotRange->{{0,80},{-1.3,1.3}}, AspectRatio-> 0.08,PlotStyle->{Darker[Green],Thickness[0.01]}]