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Browsing Mathematics / Matematik by Author "TR19429"
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Existence of Hamiltonians for some singular interactions on manifolds
Doğan, Çağlar; Erman, Fatih; Turgut, O. Teoman (American Institute of Physics Publising, 201204)The existence of the Hamiltonians of the renormalized point interactions in two and three dimensional Riemannian manifolds and that of a relativistic extension of this model in two dimensions are proven. Although it is ... 
A manybody problem with point interactions on twodimensional manifolds
Erman, Fatih; Turgut, O. Teoman (IOP Publishing, 201302)A nonperturbative renormalization of a manybody problem, where nonrelativistic bosons living on a twodimensional Riemannian manifold interact with each other via the twobody Dirac delta potential, is given by the help ... 
Nondegeneracy of the ground state for nonrelativistic Lee model
Erman, Fatih; Malkoç, Berkin; Turgut, Osman Teoman (American Institute of Physics Publising, 201408)In the present work, we first briefly sketch the construction of the nonrelativistic Lee model on Riemannian manifolds, introduced in our previous works. In this approach, the renormalized resolvent of the system is expressed ... 
On scattering from the onedimensional multiple Dirac delta potentials
Erman, Fatih; Gadella, Manuel; Uncu, Haydar (Institute of Physics Publishing, 201803)In this paper, we propose a pedagogical presentation of the LippmannSchwinger equation as a powerful tool, so as to obtain important scattering information. In particular, we consider a onedimensional system with a ... 
On the number of bound states of point interactions on hyperbolic manifolds
Erman, Fatih (World Scientific Publishing, 201701)We study the bound state problem for N attractive point Dirac δinteractions in two and threedimensional Riemannian manifolds. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit ... 
Recursion formula for the Green's function of a Hamiltonian for several types of Dirac deltafunction potentials in curved spaces
Erman, Fatih (TÜBİTAK, 2016)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 ... 
Renormalization of Dirac delta potentials through minimal extension of Heisenberg algebra
Erman, Fatih (IOP Publishing, 201709)We renormalize the model of multiple Dirac delta potentials in two and three dimensions by regularizing it through the minimal extension of Heisenberg algebra. We show that the results are consistent with the other ... 
A singular onedimensional bound state problem and its degeneracies
Erman, Fatih; Gadella, Manuel; Tunalı, Seçil; Uncu, Haydar (Springer, 201708)We give a brief exposition of the formulation of the bound state problem for the onedimensional system of N attractive Dirac delta potentials, as an N× N matrix eigenvalue problem (ΦA= ωA). The main aim of this paper is ...