Mathematics / Matematik

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

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Access Right: Open AccessSubject: search.filters.subject.Green's functions

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  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Recursion Formula for the Green's Function of a Hamiltonian for Several Types of Dirac Delta-Function Potentials in Curved Spaces
    (TUBITAK, 2016) Erman, Fatih; Erman, Fatih; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In this short article, we nonperturbatively derive a recursive formula for the Green's function associated with finitely many point Dirac delta potentials in one dimension. We extend this formula to the one for the Dirac delta potentials supported by regular curves embedded in two-dimensional manifolds and for the Dirac delta potentials supported by two-dimensional compact manifolds embedded in three-dimensional manifolds. Finally, this formulation allows us to find the recursive formula of the Green's function for the point Dirac delta potentials in two- and three-dimensional Riemannian manifolds, where the renormalization of coupling constant is required.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Computing the Electric and Magnetic Matrix Green's Functions in a Rectangular Parallelepiped With a Perfect Conducting Boundary
    (Hindawi Publishing Corporation, 2014) Yakhno, Valery; Ersoy, Şengül; 01. Izmir Institute of Technology
    A method for the approximate computation of frequency-dependent magnetic and electric matrix Green's functions in a rectangular parallelepiped with a perfect conducting boundary is suggested in the paper. This method is based on approximation (regularization) of the Dirac delta function and its derivatives, which appear in the differential equations for magnetic and electric Green's functions, and the Fourier series expansion meta-approach for solving the elliptic boundary value problems. The elements of approximate Green's functions are found explicitly in the form of the Fourier series with a finite number of terms. The convergence analysis for finding the number of the terms is given. The computational experiments have confirmed the robustness of the method.