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 | Size | Format | |
---|---|---|---|
1-s2.0-S0003491623002701-main.pdf | 570.27 kB | Adobe PDF | View/Open |
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.