Erman, FGadella, MTunalı, SeçilUncu, H2021-05-032021-05-032017-08-012190-5444https://hdl.handle.net/11411/3612https://doi.org/10.1140/epjp/i2017-11613-7We 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 (?A= ?A). 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 ? 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. © 2017, Società Italiana di Fisica and Springer-Verlag GmbH Germany.eninfo:eu-repo/semantics/openAccessArticle2-s2.0-8502788626710.1140/epjp/i2017-11613-7Q2WOS:000407709000002