QUANTUM PARTICLE IN ONE-DIMENSIONAL POTENTIALS WITH INCOMMENSURATE PERIODS

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 Hg3-δAsF6) and to the fine structure of de Haas-van Alphen oscillations. © 1979 The American Physical Society.