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

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, dive...

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Bibliographic Details
Published in:Russian journal of mathematical physics 2011-03, Vol.18 (1), p.33-53
Main Authors: Brüning, J., Dobrokhotov, S. Yu, Sekerzh-Zen’kovich, S. Ya, Tudorovskiy, T. Ya
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary: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.
ISSN:1061-9208
1555-6638
DOI:10.1134/S1061920811010055