Functional Analysis and Its Applications

, Volume 9, Issue 4, pp 279–289 | Cite as

The one-dimensional Schrödinger equation with a quasiperiodic potential

  • E. I. Dinaburg
  • Ya. G. Sinai


Functional Analysis Quasiperiodic Potential 
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Literature Cited

  1. 1.
    F. Bloch, "Über die Quantenmechanik der Elektronen in Kristallgittern," Z. Physik,52, 555–560 (1928).Google Scholar
  2. 2.
    E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford University Press (1962).Google Scholar
  3. 3.
    A. M. Dykhne, "Quasiclassical particle in one-dimensional periodic potential," Zh. Eksperim. i Teor. Fiz.,40, No. 5, 1423–1426 (1961).Google Scholar
  4. 4.
    S. G. Simonyan, "Asymptotic properties of the width of gaps in the spectrum of the Sturm—Liouville operator with a periodic potential," Differents. Uravnen.,6, No. 7, 1265–1272 (1970).Google Scholar
  5. 5.
    V. F. Lazutkin and T. F. Pankratova, "Asymptotic properties of the width of gaps in the spectrum of the Sturm—Liouville operator with a periodic potential," Dokl. Akad. Nauk SSSR,215, No. 5, 1048–1051 (1974).Google Scholar
  6. 6.
    V. I. Arnol'd, "Small denominators and the problem of stability of motion in classical and celestial mechanics," Usp. Matem. Nauk,18, No. 6, 91–192 (1963).Google Scholar
  7. 7.
    S. P. Novikov, "The periodic problem for the Kortweg—DeVries equation, I," Funktsional. Analiz i Ego Prilozhen.,8, No. 3, 54–66 (1974).Google Scholar
  8. 8.
    N. N. Bogolyubov, Yu. A. Mitropol'skii, and A. M. Samoilenko, Method of Faster Convergence in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1969).Google Scholar
  9. 9.
    É. G. Belaga, "Reducibility of systems of ordinary differential equations in the neighborhood of almost periodic motion," Dokl. Akad. Nauk SSSR,143, No. 2, 255–258 (1962).Google Scholar
  10. 10.
    J. Moser, "Perturbation theory for almost periodic solutions for nonlinear differential equations," Intern. Symposium Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York (1963).Google Scholar
  11. 11.
    J. Moser, "A new technique for the construction of solutions of nonlinear differential equations," Proc. National Academy of Sci. USA,47 (1961).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • E. I. Dinaburg
  • Ya. G. Sinai

There are no affiliations available

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