Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article On the Number of Bound States of Semirelativistic Hamiltonian With Dirac Delta Potentials in One Dimension(National Research Council of Canada, 2018) Erman, FatihWe study the bound state problem for semirelativistic N attractive Dirac delta-potentials in one dimension. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit criterion for it.Article Citation - WoS: 3Citation - Scopus: 3A Perturbative Approach To the Tunneling Phenomena(Frontiers Media S.A., 2019) Erman, Fatih; Turgut, Osman TeomanThe double-well potential is a good example, where we can compute the splitting in the bound state energy of the system due to the tunneling effect with various methods, namely path-integral, WKB, and instanton calculations. All these methods are non-perturbative and there is a common belief that it is dif fi cult to fi nd the splitting in the energy due to the barrier penetration from a perturbative analysis. However, we will illustrate by explicit examples including singular potentials (e.g., Dirac delta potentials supported by points and curves and their relativistic extensions) it is possible to fi nd the splitting in the bound state energies by developing some kind of perturbation method.Article Citation - WoS: 16Citation - Scopus: 15On Scattering From the One-Dimensional Multiple Dirac Delta Potentials(Institute of Physics Publishing, 2018) Erman, Fatih; Gadella, Manuel; Uncu, HaydarIn this paper, we propose a pedagogical presentation of the Lippmann-Schwinger equation as a powerful tool, so as to obtain important scattering information. In particular, we consider a one-dimensional system with a Schrödinger-type free Hamiltonian decorated with a sequence of N attractive Dirac delta interactions. We first write the Lippmann-Schwinger equation for the system and then solve it explicitly in terms of an N × N matrix. Then, we discuss the reflection and the transmission coefficients for an arbitrary number of centres and study the threshold anomaly for the N = 2 and N = 4 cases. We also study further features like the quantum metastable states and resonances, including their corresponding Gamow functions and virtual or antibound states. The use of the Lippmann-Schwinger equation simplifies our analysis enormously and gives exact results for an arbitrary number of Dirac delta potentials.