Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

Browse

Filters

2017 - 20203

Settings

Author: search.filters.author.Uncu, HaydarWoS Q: search.filters.wosQuartile.Q2

Search Results

Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    The Propagators for Δ and Δ′ Potentials With Time-Dependent Strengths
    (Frontiers Media S.A., 2020) Erman, Fatih; Gadella, Manuel; Uncu, Haydar
    We study the time-dependent Schrodinger equation with finite number of Dirac delta and delta ' potentials with time dependent strengths in one dimension. We obtain the formal solution for generic time dependent strengths and then we study the particular cases for single delta potential and limiting cases for finitely many delta potentials. Finally, we investigate the solution of time dependent Schrodinger equation for delta ' potential with particular forms of the strengths.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Green's Function Formulation of Multiple Nonlinear Dirac Delta-Function Potential in One Dimension
    (Elsevier, 2020) Erman, Fatih; Uncu, Haydar
    In this work, we study the scattering problem of the general nonlinear finitely many Dirac delta potentials with complex coupling constants (or opacities in the context of optics) using the Green's function method and then find the bound state energies and the wave functions for the particular form of the nonlinearity in the case of positive real coupling constants. (C) 2020 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 16
    A Singular One-Dimensional Bound State Problem and Its Degeneracies
    (Springer Verlag, 2017) Erman, Fatih; Gadella, Manuel; Tunalı, Seçil; Uncu, Haydar
    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.