Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Completeness Relation in Renormalized Quantum Systems(Frontiers Media SA, 2025) Erman, F.; Turgut, O.T.In this work, we show that the completeness relation for the eigenvectors, which is an essential assumption of quantum mechanics, remains true if the Hamiltonian, having a discrete spectrum, is modified by a delta potential (to be made precise by a renormalization scheme) supported at a point in two- and three-dimensional compact manifolds or Euclidean spaces. The formulation can be easily extended to an (Formula presented.) center case and the case where delta interaction is supported on curves in the plane or space. We finally give an interesting application for the sudden perturbation of the support of the delta potential. © © 2025 Erman and Turgut.Article Explicit Derivation of the Propagator for a Point Interaction in Three Dimensional Hyperbolic Space(Springer/plenum Publishers, 2024) Erman, FatihThe explicit expression for the propagator of the Dirac delta potential in three dimensional hyperbolic spaces is derived using the integral transform of the Krein's type of the resolvent formula, obtained after the renormalization procedure.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: 4Citation - Scopus: 5On the Number of Bound States of Point Interactions on Hyperbolic Manifolds(World Scientific Publishing Co. Pte Ltd, 2017) Erman, FatihWe study the bound state problem for N attractive point Dirac δ-interactions in two- and three-dimensional Riemannian manifolds. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit criterion for it in hyperbolic manifolds ℍ2 and ℍ3. Furthermore, we study the same spectral problem for a relativistic extension of the model on ℝ2 and ℍ2.