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

Abstract

In the paper, which is the second part of the paper by J. Bruning, S. Dobrokhotov, S. Sekerzh-Zenkovich, T. Tudorovskiy, “Spectral series of the Schrodinger 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 Schrodinger 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.