f[n_,x_]:=((Abs[((((((1/π)))^(1/4)) (E^(-((x^2)/2))) HermiteH[n,x])/(Sqrt[(2^n) n!]))])^2)

GraphicsGrid[Partition[Table[Plot[Evaluate[Append[Table[f[n,x]+n+(1/2),{n,0,7}],((x^2)/2)]],{x,-4,4},Filling->Table[{i->{i-(1/2),Orange}},{i,1,8}],Mesh->All,MaxRecursion->rr,PlotPoints->7],{rr,0,3}],2],ImageSize->700]