The energy spectrum and wave functions for a particle in periodic potentials with incommensurate periods are obtained analytically and reduced to specific phase trajectories. The spectrum is of the devil's-stairs type. States may be extended and localized, separated by mobility edges. These results are applicable to incommensurate linear chain structures (such as those in Hg_3-δAsF₆) and to the fine structure of de Haas-van Alphen oscillations.
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M. Ya. Azbel (1979) studied this question.
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