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Bloch spectrum

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

where U<sub>α</sub> 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&nbsp;−&nbsp;E)φ = 0 are bounded on the whole real axis. The Bloch spectrum consists of the half-line E<sub>0</sub>&nbsp;<&nbsp;E from which certain closed intervals [E<sub>2j−1</sub>,&nbsp;E<sub>2j</sub>] (j = 1, 2, ...) are omitted. These are forbidden bands (or gaps) so the (E<sub>2j−2</sub>,&nbsp;E<sub>2j−1</sub>) are allowed bands.

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