where U α is a periodic function of period α. The Bloch spectrum of H is defined as the set of values E for which all the solutions of (H − E)φ = 0 are bounded on the whole real axis. The Bloch spectrum consists of the half-line E 0 < E from which certain closed intervals [ E 2 j −1, E 2 j ] (j = 1, 2,...) are omitted. These are forbidden bands (or gaps) so the (E 2 j −2, E 2 j −1) are allowed bands.