Geodesic
Quantum particle in a one-dimensional deformed lattice. Estimates of the gaps in the spectrum
Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 3, pp. 344-357 
E. D. Belokolos. Quantum particle in a one-dimensional deformed lattice. Estimates of the gaps in the spectrum. Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 3, pp. 344-357. http://geodesic.mathdoc.fr/item/TMF_1975_25_3_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the potential of oscillating lattice at fixed moment of time is a quasi-periodical function. Stationary states of quantum particle in quasi-periodical potential satisfy the generalized Floquet–Bloch theorem and can be characterized by the quasi-momentum which is connected with the density of states exactly in the same way as in the case of the particle in a purely periodical potential. If the quasi-momentum satisfies the generalized Bragg–Woolfe conditions, the spectrum may include the lacunae (forbidden zones), for the sizes of which the estimates are given.

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