(*The ground state for the Morse and harmonic potentials*)

alpha=1.
miu=1.
DD=10.
a=Sqrt[2*miu*DD]/alpha
za=2*a*Exp[-alpha*x]
Vx=DD*Exp[-alpha*x]*(Exp[-alpha*x]-2.)(*potencjal Morsea*)
F0=0.5/20*Exp[-za/2]*za^(a-0.5) (*the function has been arbitrarily multiplied by 10 for typographical reasons*)
kharm=2*alpha^2*DD
Vharm=kharm/2*x^2-DD
alphaharm=Sqrt[kharm*miu]
Nnormharm=Sqrt[Sqrt[alphaharm/Pi]]
F0harm=Nnormharm*Exp[-alphaharm*x^2/2]
Plot[{Vx,10*F0,Vharm,10*F0harm},{x,-1.5,1.5},PlotStyle->{{Thickness[0.005],GrayLevel[0.1]},
{Thickness[0.005],GrayLevel[0.1]},{Thickness[0.006],GrayLevel[0.6],Dashed},
{Thickness[0.006],GrayLevel[0.6],Dashed}}] (*potencjał i ground state, Morse and harmonic; the function has been arbitrarily multiplied by 10 for typographical reasons*)