SPECTRAL AND SCATTERING THEORY FOR THE AHARONOV–BOHM OPERATORS

DOI10.1142/S0129055X11004205zbMath1230.81054arXiv0911.4715OpenAlexW2091617432MaRDI QIDQ3011491

Serge Richard, Konstantin Pankrashkin

Publication date: 29 June 2011

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.4715

zbMATH Keywords

boundary triplespectral and scattering theorywave and scattering operatorsAharonov-Bohm model

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Scattering theory for PDEs (35P25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) (S)-matrix theory, etc. in quantum theory (81U20) Scattering theory of linear operators (47A40)

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Cites Work

• Unnamed Item
• Unnamed Item
• The one-dimensional Schrödinger operator with point \(\delta \) - and \(\delta \) -interactions
• High-velocity estimates for the scattering operator and Aharonov-Bohm effect in three dimensions
• The Aharonov-Bohm effect and scattering theory
• Time-delay in potential scattering theory. Some geometric results
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• On the Aharonov-Bohm Hamiltonian
• Resolvents of self-adjoint extensions with mixed boundary conditions
• Hermitian symplectic geometry and extension theory
• The Aharonov$ndash$Bohm effect and time-dependent inverse scattering theory
• Significance of Electromagnetic Potentials in the Quantum Theory
• SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS
• Weber–Schafheitlin-type integrals with exponent 1
• Aharonov–Bohm effect with δ-type interaction
• Magnetic scattering at low energy in two dimensions
• Generalized boundary conditions for the Aharonov–Bohm effect combined with a homogeneous magnetic field
• Scattering on compact manifolds with infinitely thin horns
• A remark on Krein's resolvent formula and boundary conditions