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The spectrum and solutions of the 1-D Schrödinger equation with a quasiperiodic potential V are investigated numerically. Quasiperiodicity, in contrast to periodicity, makes the localisation of modes possible. V is taken as the sum of two incommensurate periodic delta-function series. The spectrum consists of bands separated by gaps which correspond to plateaus in the winding number. The spectrum of extended solutions (three-frequency-quasiperiodic) is found from the initial value problem. Localised solutions cannot be found in this way owing to numerical instability. Instead, localised solutions (exponential decay on both sides) and the concomitant point spectrum are obtained from a boundary value method. An alternative method to find the point spectrum for bounded potentials is proved to be also valid for the delta-function potentials used. Connections with the MHD spectrum of toroidal plasmas are pointed out.

Additional information

Authors: SALAT A, Max-Planck-Institut für Plasmaphysik, Garching bei München (DE)
Bibliographic Reference: Article: Physical Review A (1991) 23 pp.
Availability: Available from Max-Planck-Institut für Plasmaphysik, 8046 Garching bei München (DE)
Record Number: 199111179 / Last updated on: 1994-12-02
Original language: en
Available languages: en