Resolvents of self-adjoint extensions with mixed boundary conditions

Abstract

We prove a variant of Krein's resolvent formula expressing the resolvents of self-adjoint extensions through the associated boundary conditions. Applications to solvable quantum-mechanical problems are discussed.

15 pages, rewritten almost completely

References in corpus (10)

• Global Theory of Quantum Boundary Conditions and Topology Change
• Scattering on compact manifolds with infinitely thin horns
• Bound states in straight quantum waveguides with combined boundary conditions
• Exponential splitting of bound states in a waveguide with a pair of distant windows
• Boundary triples and Weyl functions for singular perturbations of self-adjoint operators
• A remark on Krein's resolvent formula and boundary conditions
• Isospectral domains with mixed boundary conditions
• On-diagonal singularities of the Green functions for Schroedinger operators
• The hybrid spectral problem and Robin boundary conditions
• Reducible boundary conditions in coupled channels

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• General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation
• The Maslov Index and the Spectra of Second Order Elliptic Operators
• The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions
• Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration
• Point Interaction Hamiltonians in Bounded Domains
• Resonances in Models of Spin Dependent Point Interactions
• Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations
• Supersymmetric Descendants of Self-Adjointly Extended Quantum Mechanical Hamiltonians
• Wave operators, similarity and dynamics for a class of Schroedinger operators with generic non-mixed interface conditions in 1D
• Boundary pairs associated with quadratic forms
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• First-order asymptotic perturbation theory for extensions of symmetric operators
• Adiabatic evolution of 1D shape resonances: an artificial interface conditions approach
• Eigenvalue statistics for Schrödinger operators with random point interactions on ${\mathbb{R}}^d$, $d=1,2,3$
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• ${\mathsf{D}}^2=\mathsf{H}+1/4$ with point interactions