Russian Journal of Mathematical Physics

, Volume 18, Issue 1, pp 33–53 | Cite as

Spectral series of the Schrödinger operator in a thin waveguide with a periodic structure. 2. Closed three-dimensional waveguide in a magnetic field

  • J. Brüning
  • S. Yu. Dobrokhotov
  • S. Ya. Sekerzh-Zen’kovich
  • T. Ya. Tudorovskiy


In the paper, which is the second part of the paper by J. Brüning, S. Dobrokhotov, S. Sekerzh-Zenkovich, T. Tudorovskiy, “Spectral series of the Schrödinger operator in thin waveguides with a periodic structure. 1,” Russ. J. Math. Phys. 13 (4), 401–420 (2006), using the adiabatic approximation, diverse quantum states of the stationary Schrödinger equation for a particle in a thin waveguide in a magnetic field are constructed. The problems of “destruction” of the adiabatic approximation as the value of energy increases and of replacing this approximation by the approximation of V. P. Maslov’s theory of complex germ (the complex WKB method) are studied.


Mathematical Physic Spectral Problem Adiabatic Approximation Trap Mode Spectral Series 
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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • J. Brüning
    • 1
  • S. Yu. Dobrokhotov
    • 2
  • S. Ya. Sekerzh-Zen’kovich
    • 3
  • T. Ya. Tudorovskiy
    • 4
  1. 1.Humboldt UniversityBerlinGermany
  2. 2.Institute for Problems in MechanicsRAS, Moscow Institute of Physics and TechnologyMoscowRussia
  3. 3.Institute for Problems in MechanicsRASMoscowRussia
  4. 4.Institute for Molecules and MaterialsRadboud University of NijmegenNijmegenRussia

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