Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Erman, FatihSubject: search.filters.subject.Quantum mechanics

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  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    A Direct Method for the Low Energy Scattering Solution of Delta Shell Potentials
    (Springer, 2022) Erman, Fatih; Seymen, Sema
    A direct method for the bound states and the low energy scattering from a circular and a spherical delta shell potentials is proposed, and the results are compared with the one using the standard partial wave analysis developed for potentials with rotational symmetry. The formulation is presented in momentum space, and the scattering solutions are obtained by considering the elementary use of distributions. In this approach, the outgoing boundary conditions are imposed explicitly in contrast to the iϵ prescription often used in quantum mechanics.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    A Many-Body Problem With Point Interactions on Two-Dimensional Manifolds
    (IOP Publishing Ltd., 2013) Erman, Fatih; Turgut, O. Teoman
    A non-perturbative renormalization of a many-body problem, where non-relativistic bosons living on a two-dimensional Riemannian manifold interact with each other via the two-body Dirac delta potential, is given by the help of the heat kernel defined on the manifold. After this renormalization procedure, the resolvent becomes a well-defined operator expressed in terms of an operator (called principal operator) which includes all the information about the spectrum. Then, the ground state energy is found in the mean-field approximation and we prove that it grows exponentially with the number of bosons. The renormalization group equation (or Callan-Symanzik equation) for the principal operator of the model is derived and the beta function is exactly calculated for the general case, which includes all particle numbers.