When nearing the edges of the lattice, there are problems with the boundary condition. Therefore, we can represent the ion lattice as a ring following the Born–von Karman boundary conditions. If L is the length of the lattice so that L ≫ a, then the number of ions in the lattice is so big, that when considering one ion, its surrounding is almost linear, and the wavefunction of the electron is unchanged. So now, instead of two boundary conditions we get one circular boundary condition: ψ ψ ( 0 ) = ψ ψ ( L ) .