Spectra of self-adjoint extensions and applications to solvable Schroedinger operators

TL;DR

This paper presents a comprehensive theory of self-adjoint extensions using boundary triples, describing their spectra via Krein maps, with applications to quantum graphs, point interactions, and singular perturbations.

Contribution

It provides a self-contained framework for analyzing spectra of self-adjoint extensions with new applications to various quantum systems.

Findings

Spectra of self-adjoint extensions characterized by Krein maps.

Unified boundary triple approach for different quantum models.

Applications to quantum graphs and singular perturbations.

Abstract

We give a self-contained presentation of the theory of self-adjoint extensions using the technique of boundary triples. A description of the spectra of self-adjoint extensions in terms of the corresponding Krein maps (Weyl functions) is given. Applications include quantum graphs, point interactions, hybrid spaces, singular perturbations.