Problem 2 (b)

W=Exp[-((((X -(d/γ))(E^(γ t))+(d/γ)))^2)-(((P (E^(-γ t))))^2)];
ContourPlot[W/.{d->5,γ->2,t->0},{X,-5,5},{P,-5,5},PlotRange->All]

ContourPlot[W/.{d->5,γ->2,t->0.5},{X,-5,5},{P,-5,5},PlotRange->All]

ContourPlot[W/.{d->5,γ->2,t->1},{X,-5,5},{P,-5,5},PlotRange->All]

Problem 3 (c)

ψa=((-I Ω)/(I Δ-Γ/2))(1-(E^((I Δ-Γ/2)t)));
Simplify[D[ψa,t]-ψa(I Δ-Γ/2)-I Ω]

θ=π-2Abs[ψa];
ϕ=-Arg[ψa];
SP=SphericalPlot3D[1,{x,0,Pi},{y,0,2Pi}];
PP=ParametricPlot3D[{Sin[θ]Cos[ϕ],Sin[θ]Sin[ϕ],Cos[θ]}/.{Ω->2,Δ->10,Γ->1},{t,0,5}];
Show[SP,PP]
PP=ParametricPlot3D[{Sin[θ]Cos[ϕ],Sin[θ]Sin[ϕ],Cos[θ]}/.{Ω->0.2,Δ->0.1,Γ->1},{t,0,5}];
Show[SP,PP]