I have been banned, maybe my nickname was not so kind. I let the topic continue here. I report my last comment: "Ok, I got the point. thanks for replying! It's just a change of basis that under boundary condition diagonalize the Hamiltonian. But then a subtle point: In order for k-representation to be a good basis change (i.e. orthogonality and completeness properties) I guess that one has to choose the k values AS if there were periodic boundary conditions (i.e. k=2pi*n/L). Right? Then another last point: how do you really model a finite size chain? A finite size chain has zero boundary condition. In this case I use the k representation with k chosen as if there were periodic boundary condition and just then reconstruct the physical wavefunction by making a wavepacket that is zero on the borders? "