From here we can see that also the character shall be invariant by a translation of L i : e i k 1 n 1 a 1 = e i k 1 ( n 1 a 1 + L 1 ) and from the last equation we get for each dimension a periodic condition: k 1 n 1 a 1 = k 1 ( n 1 a 1 + L 1 ) − − 2 π π m 1 where m 1 ∈ ∈ Z is an integer and k 1 = 2 π π m 1 L 1