A remark on Krein's resolvent formula and boundary conditions

DOI10.1088/0305-4470/38/22/010zbMath1071.47003arXivmath-ph/0408021OpenAlexW3102635086MaRDI QIDQ5462467

Konstantin Pankrashkin, Sergio A. Albeverio

Publication date: 2 August 2005

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0408021

zbMATH Keywords

quantum graphslinear relationsselfadjoint extensionsKrein resolvent formulaboundary value spacepoint interactions with mixed coundary conditions

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Dilations, extensions, compressions of linear operators (47A20) Linear relations (multivalued linear operators) (47A06)

Related Items (17)

Coupling in the singular limit of thin quantum waveguides ⋮ Schrödinger operators with nonlocal point interactions ⋮ Dynamics of an electron confined to a ``hybrid plane and interacting with a magnetic field ⋮ SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS ⋮ Point interaction Hamiltonians in bounded domains ⋮ Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit ⋮ ADIABATIC EVOLUTION OF 1D SHAPE RESONANCES: AN ARTIFICIAL INTERFACE CONDITIONS APPROACH ⋮ Resolvents of self-adjoint extensions with mixed boundary conditions ⋮ SPECTRAL AND SCATTERING THEORY FOR THE AHARONOV–BOHM OPERATORS ⋮ Green's function approach for quantum graphs: an overview ⋮ Edge switching transformations of quantum graphs—a scattering approach ⋮ Dynamics on a Graph as the Limit of the Dynamics on a “Fat Graph” ⋮ A ``hybrid plane with spin-orbit interaction ⋮ The Schrödinger equation on a star-shaped graph under general coupling conditions ⋮ Scale invariant effective Hamiltonians for a graph with a small compact core ⋮ Direct and Inverse Acoustic Scattering by a Collection of Extended and Point-Like Scatterers ⋮ Boundary conditions for the quantum Hall effect

This page was built for publication: A remark on Krein's resolvent formula and boundary conditions