Spectral theory for Schrödinger operators on compact metric graphs with δ and δ′ couplings : a survey

Publikationstyp
Book Part
Date Issued
2024-06-24
Sprache
English
Author(s)
Rohleder, Jonathan  
Mathematik E-10  
Seifert, Christian  orcid-logo
Mathematik E-10  
TORE-URI
https://hdl.handle.net/11420/49465
First published in
Trends in Mathematics  
Number in series
F3446
Start Page
43
End Page
89
Citation
In: Schwenninger, F.L., Waurick, M. (eds) Systems Theory and PDEs (WOSTAP 2022) Trends in Mathematics. Birkhäuser, Cham. (2024)
Contribution to Conference
Workshop on Systems Theory and PDEs, WOSTAP 2022  
Publisher DOI
10.1007/978-3-031-64991-2_3
Scopus ID
2-s2.0-85205013806
Publisher
Springer
ISSN
2297-0215
ISBN
978-3-031-64990-5
978-3-031-64991-2
Spectral properties of Schrödinger operators on compact metric graphs are studied, and special emphasis is put on differences in the spectral behavior between different classes of vertex conditions. We survey recent results especially for δ and δ′ couplings and demonstrate the spectral properties on many examples. Among other things, properties of the ground state eigenvalue and eigenfunction and the spectral behavior under various perturbations of the metric graph or the vertex conditions are considered.
Subjects
Eigenvalues
Metric graph
Quantum graph
Schrödinger operator
Surgery principles
DDC Class
510: Mathematics