For each band gap, there is one additional state. The energies of these states depend on the point of termination τ τ but not on the length N . The energy of such a state can lie either at the band edge or within the band gap. If the energy is within the band gap, the state is a surface state localized at one end of the lattice, but if the energy is at the band edge, the state is delocalized across the lattice.