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

DOI10.1134/S1061920811010055zbMath1251.35099OpenAlexW2149794499MaRDI QIDQ455561

S. Yu. Dobrokhotov, Jochen Brüning, S. Ya. Sekerzh-Zen'kovich, T. Ya. Tudorovskii

Publication date: 22 October 2012

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920811010055

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) Schrödinger operator, Schrödinger equation (35J10) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (1)

Averaging and spectral bands for the 2-D magnetic Schrödinger operator with growing and one-direction periodic potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The spectral asymptotics of the two-dimensional Schrödinger operator with a strong magnetic field. I
• Quantum and classical dynamics of an electron in thin curved tubes with spin and external electromagnetic fields taken into account
• Operator separation of variables for adiabatic problems in quantum and wave mechanics
• Spectral series of the Schrödinger operator in thin waveguides with periodic structure. I: Adiabatic approximation and semiclassical asymptotics in the 2D case
• On the construction of quasimodes associated with stable periodic orbits
• Quantum mechanics on manifolds embedded in Euclidean space.
• Effective dynamics for Bloch electrons: Peierls substitution and beyond
• Singular Bohr-Sommerfeld rules.
• The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory
• Explicit formulas for generalized action-angle variables in a neighborhood of an isotropic torus and their application
• Semiclassical analysis of constrained quantum systems
• Statistical properties of the spectra of Laplace-Beltrami operators on Liouville surfaces
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS

This page was built for publication: Spectral series of the Schrödinger operator in a thin waveguide with a periodic structure. II: Closed three-dimensional waveguide in a magnetic field