A remark on Krein's resolvent formula and boundary conditions

2004/08/12 by Sergio Albeverio, Konstantin Pankrashkin · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics #math-ph #math.FA #math.MP #msc:46N50 #msc:47A06 #msc:47A10

paper · pdf · doi:10.1088/0305-4470/38/22/010

published as J. Phys. A: Math. Gen. 38 (2005) 4859-4864 · 6 pages

arxiv created 2004/08/12 · openalex publication_date 2005/05/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Kirchhoff's rule for quantum wires

Cited by

• MUSIC algorithm for locating point-like scatterers with multiple interactions
• Geometry-induced Coulomb-like potential in helically twisted quantum systems

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