The Bloch spectrum is a concept in quantum mechanics in the field of theoretical physics; this concept addresses certain energy spectrum considerations. Let H be the one-dimensional Schrödinger equation operator
H = − d 2 d x 2 + U α , {\displaystyle H=-{\frac {d^{2}}{dx^{2}}}+U_{\alpha },}
where Uα 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 E0 < E from which certain closed intervals [E2j−1, E2j] (j = 1, 2, ...) are omitted. These are forbidden bands (or gaps) so the (E2j−2, E2j−1) are allowed bands.
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