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Bloch spectrum : ウィキペディア英語版
Bloch spectrum

The Bloch spectrum is a concept in quantum mechanics in the field of theoretical physics; this concept addresses certain energy spectra considerations.
Let ''H'' be the one-dimensional Schrödinger equation operator
: H = - \frac + U_\alpha,
where ''Uα'' 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 ''E''0 < ''E'' from which certain closed intervals () (''j'' = 1, 2, ...) are omitted. These are forbidden bands (or gaps) so the (''E''2''j''−2, ''E''2''j''−1) are allowed bands.
== References ==



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