(* Potencial de Woods-Saxon *)

V[x_]:=-(U/((E^(((x-a))^2))+1));U=7.;a=2.;
Plot[V[x],{x,0.01,10},PlotRange->All]

(* Busqueda de Estados Ligados *)

Ener=-3;
solution2=NDSolve[{-(1./2.)* y''[x] + V[x] y[x]==Ener *y[x] , 
y'[0.]==1,y[0.]==0.},y,{x,0,20}]
Plot[Evaluate[{y[x]}/.solution2],{x,0,20}]

(* Busqueda automatica de estados ligados*)

Manipulate[
solution2=NDSolve[{-(1./2.)* y''[x] + V[x] y[x]==Ener *y[x] , 
y'[0.]==1,y[0.]==0.},y,{x,0,20}] ;
Plot[Evaluate[{y[x]}/.solution2],{x,0,20}] , 

{ {Ener,-3,"Energy"},-3,-2, -0.05,Appearance->"Labeled"}]

Ajuste fino

Manipulate[
solution2=NDSolve[{-(1./2.)* y''[x] + V[x] y[x]==Ener *y[x] , 
y'[0.]==1,y[0.]==0.},y,{x,0,20}] ;
Plot[Evaluate[{y[x]}/.solution2],{x,0,10}, PlotRange->{-5,5}] , 

{ {Ener,-2.6,"Energy"},-3,-2, -0.00005,Appearance->"Labeled"}]