Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/7092
Title: On scattering from the one-dimensional multiple Dirac delta potentials
Authors: Erman, Fatih
Gadella, Manuel
Uncu, Haydar
Keywords: Dirac delta potentials
Gamow states
Lippmann-Schwinger equation
Resonances
Threshold anomalies
Virtual state
Issue Date: Mar-2018
Publisher: Institute of Physics Publishing
Source: Erman, F., Gadella, M., and Uncu, H. (2018). On scattering from the one-dimensional multiple Dirac delta potentials. European Journal of Physics, 39(3). doi:10.1088/1361-6404/aaa8a3
Abstract: In 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.
URI: http://doi.org/10.1088/1361-6404/aaa8a3
http://hdl.handle.net/11147/7092
ISSN: 0143-0807
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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