Abstract
The paper considers the Schrödinger equation for a single particle and its discrete analogues. Assuming that the coefficients of these equations are homogeneous and ergodic random fields, it is proved that the spectra of corresponding random operators and their point spectra are dense with probability 1 and that in the one-dimensional case they have no absolutely continuous component. Rather wide sufficient conditions of exponential growth of the Cauchy solutions of the one-dimensional equations considered are found.
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Communicated by Ya. G. Sinai
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Pastur, L.A. Spectral properties of disordered systems in the one-body approximation. Commun.Math. Phys. 75, 179–196 (1980). https://doi.org/10.1007/BF01222516
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DOI: https://doi.org/10.1007/BF01222516