A remark on Krein's resolvent formula and boundary conditions

Abstract

We prove an analog of Krein's resolvent formula expressing the resolvents of self-adjoint extensions in terms of boundary conditions. Applications to quantum graphs and systems with point interactions are discussed.

arXiv comment6 pages

References in corpus (3)

• Kirchhoff's Rule for Quantum Wires
• Scattering on compact manifolds with infinitely thin horns
• An approximation to ${\delta }^{\prime }$ couplings on graphs

Cited by in corpus (17)

• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Coupling in the singular limit of thin quantum waveguides
• Resolvents of self-adjoint extensions with mixed boundary conditions
• Green's function approach for quantum graphs: an overview
• Nonlinear Dirac Equation On Graphs With Localized Nonlinearities: Bound States And Nonrelativistic Limit
• A "hybrid plane" with spin-orbit interaction
• Spin dependent point potentials in one and three dimensions
• Boundary conditions: The path integral approach
• Point Interaction Hamiltonians in Bounded Domains
• Dynamics of an electron confined to a "hybrid plane" and interacting with a magnetic field
• Resonances in Models of Spin Dependent Point Interactions
• Reducible boundary conditions in coupled channels
• Edge switching transformations of quantum graphs
• Boundary conditions for the quantum Hall effect
• Spectrum of a family of spin-orbit coupled Hamiltonians with singular perturbation
• Krein's Formula And Heat-Kernel Expansion For Some Differential Operators With A Regular Singularity