V[x_]:=0; (* CHANGE this to any function of x that you want for your well *)
Manipulate[sol=First[NDSolve[{((-(197^2))/(2 511000))ψ''[x]+V[x] ψ[x]==energy ψ[x],
ψ[0]==0,
ψ'[0]==1},{ψ},{x,0,1}]];
Plot[ψ[x]/.sol,{x,0,1}],{energy,0,5 (* CHANGE these limits if your well has a different floor *)}]