Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/14022
Title: On Schrödinger operators modified by δ interactions
Authors: Akbaş, Kaya Güven
Erman, Fatih
Turgut, O. Teoman
Keywords: Dirac δ interaction
Green's function
Point interaction
Renormalization
Schrödinger operator
Spectrum
Publisher: Academic Press
Abstract: We study the spectral properties of a Schrödinger operator H0 modified by δ interactions and show explicitly how the poles of the new Green's function are rearranged relative to the poles of original Green's function of H0. We prove that the new bound state energies are interlaced between the old ones, and the ground state energy is always lowered if the δ interaction is attractive. We also derive an alternative perturbative method of finding the bound state energies and wave functions under the assumption of a small coupling constant in a somewhat heuristic manner. We further show that these results can be extended to cases in which a renormalization process is required. We consider the possible extensions of our results to the multi center case, to δ interaction supported on curves, and to the case, where the particle is moving in a compact two-dimensional manifold under the influence of δ interaction. Finally, the semi-relativistic extension of the last problem has been studied explicitly. © 2023 Elsevier Inc.
URI: https://doi.org/10.1016/j.aop.2023.169468
https://hdl.handle.net/11147/14022
ISSN: 0003-4916
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Files in This Item:
File SizeFormat 
1-s2.0-S0003491623002701-main.pdf570.27 kBAdobe PDFView/Open
Show full item record



CORE Recommender

SCOPUSTM   
Citations

1
checked on Dec 7, 2024

WEB OF SCIENCETM
Citations

1
checked on Oct 26, 2024

Page view(s)

186
checked on Dec 2, 2024

Download(s)

72
checked on Dec 2, 2024

Google ScholarTM

Check




Altmetric


Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.