Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Perturbative and Exact Analysis of Point Interactions(01. Izmir Institute of Technology, 2021) Altınbaşak, Ezgi; Erman, FatihIn this thesis, a general formulation for the bound state energies of a finite number of attractive Dirac delta potentials is given in terms of a finite dimensional matrix. The stationary scattering problem is also studied using the distributional solutions of algebraic equations in momentum space. Finally, the energy gap and splitting for the bound state energies when the distance between the delta potentials is large is approximately calculated using a kind of perturbation theory.Master Thesis Two-Particle Schrodinger Operators With Point Interactions(01. Izmir Institute of Technology, 2020) Kızılkaya, Melih; Erman, FatihIn this thesis, a singular quantum mechanical problem, where two particles interact with each other through Dirac delta potentials in the plane, has been considered. The proof for the existence of a self-adjoint Hamiltonian operator for the model is given by using some operator theory techniques and renormalization idea in quantum field theory. Moreover, some necessary background for unbounded operators is reviewed in order to make the thesis as self-contained as possible.Master Thesis Point Interactions in Quantum Mechanics(Izmir Institute of Technology, 2014) Tunalı, Seçil; Erman, FatihIn this thesis, the point interactions in quantum mechanics in the context of renormalization are reviewed. Some spectral properties for special configuration of the centers of point interactions are given in detail. Also, the isotropic harmonic oscillator with point interaction in one dimension and in two dimensions are discussed shortly.Master Thesis Solitonic Solutions and Particle Localization in Higher Dimensional Spaces(Izmir Institute of Technology, 2003) Erman, Fatih; Erdem, RecaiFirst the basic extra dimensional theory (i.e. Kaluza-Klein theory) and the main aspects of solitons are reviewed. Then the current status of extra dimen-sional models and the application of solitons (especially kinks) in this context are studied. The extra dimensional models for fermion localization are considered with a particular emphasis. Finally a variation of these models which tries to in-corporate the best aspects of various models for fermion localization is presented.