Solucion de la Ecuacion de Schrodinger independiente del Tiempo

V[x_] := 
          U/(E^((x - a)^2) + 1);  U = 7. ; a = 2. ;

Plot[-V[x], {x, 0.01, 10},  PlotRange -> All]

k = I 1;
solution2=NDSolve[{-1. /2. *y''[x]-V[x]*y[x]==k^2/2. *y[x],y'[0.]==1,y[0. ] == 0. },y,{x, 0, 20}]
Plot[Evaluate[{y[x]/x} /. solution2], {x, 0, 20}]

k = I 2;
solution2=NDSolve[{-1. /2. *y''[x]-V[x]*y[x]==k^2/2. *y[x],y'[0.]==1,y[0. ] == 0. },y,{x, 0, 20}]
Plot[Evaluate[{y[x]/x} /. solution2], {x, 0, 20}]

Nsteps  =  
            10 ;
kmax  =  
        1.5;
kmin  =  
        1.3;
deltak  =  (kmax  -  kmin)/
        Nsteps
For [i = 0, i <  Nsteps, 
    i++;
   k =  (1  +  i/Nsteps );
solution2=NDSolve[{-1. /2. *y''[x]-V[x]*y[x]==- (k^2/2. )*y[x],y'[0.]==1,y[0. ] == 0. },y,{x, 0, 20}];
Plot[
              Evaluate[{y[x]} /. solution2], {x, 0, 20}] ;
      ]