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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 |
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 |
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