Bloch spectrum

{{Short description|Concept in quantum mechanics}}

{{Refimprove|date=December 2008}}

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

:$H\; =\; -\; \backslash frac\{d^2\}\{dx^2\}\; +\; U\_\backslash alpha,$

where U_α is a periodic function of period α. The Bloch spectrum"An upper bound on the allowed bands of the Bloch spectrum of one-dimensional Schrödinger operators with periodic potentials", N. N. Meiman, Journal of Mathematical Physics, March, 1983, volume 24, issue 3, pp. 539–540 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 [E_2j−1, E_2j] (j = 1, 2, ...) are omitted. These are forbidden bands (or gaps) so the (E_2j−2, E_2j−1) are allowed bands.