Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/6472
Title: A singular one-dimensional bound state problem and its degeneracies
Authors: Erman, Fatih
Gadella, Manuel
Tunalı, Seçil
Uncu, Haydar
Keywords: One-dimensional system
Dirac delta potentials
Perron-Frobenius theorem
Cauchy interlacing theorem
Issue Date: Aug-2017
Publisher: Springer Verlag
Source: Erman, F., Gadella, M., Tunalı, S., and Uncu, H. (2017). A singular one-dimensional bound state problem and its degeneracies. European Physical Journal Plus, 132(8). doi:10.1140/epjp/i2017-11613-7
Abstract: We give a brief exposition of the formulation of the bound state problem for the one-dimensional system of N attractive Dirac delta potentials, as an N× N matrix eigenvalue problem (ΦA= ωA). The main aim of this paper is to illustrate that the non-degeneracy theorem in one dimension breaks down for the equidistantly distributed Dirac delta potential, where the matrix Φ becomes a special form of the circulant matrix. We then give elementary proof that the ground state is always non-degenerate and the associated wave function may be chosen to be positive by using the Perron-Frobenius theorem. We also prove that removing a single center from the system of N delta centers shifts all the bound state energy levels upward as a simple consequence of the Cauchy interlacing theorem.
URI: http://doi.org/10.1140/epjp/i2017-11613-7
http://hdl.handle.net/11147/6472
ISSN: 2190-5444
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 Description SizeFormat 
6472.pdfMakale452.13 kBAdobe PDFThumbnail
View/Open
Show full item record



CORE Recommender

SCOPUSTM   
Citations

15
checked on Mar 1, 2024

WEB OF SCIENCETM
Citations

14
checked on Feb 26, 2024

Page view(s)

1,190
checked on Mar 4, 2024

Download(s)

188
checked on Mar 4, 2024

Google ScholarTM

Check




Altmetric


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