Browsing by Author "Beker, Haluk."
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Item Approximate ground state energies of one dimensional potential wells by the s-matrix formalism(Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2003., 2003.) Erkol, Hakan.; Beker, Haluk.One dimensional potential wells are described as a collection of consecutive thin slices, each approximated by a Dirac delta well. Bound state energies of these Dirac delta well conglomerates are calculated, using a method based on Transfer and S-Matrix formalisms. It is observed that the method, a variant of the Born approximation, works best for the ground state energies of narrow and shallow wells. The approximate results compare favorably with the known exact results of several potential well problems.Item Deforming SO(4,2) generators(Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.) Kılıç, Delalcan.; Beker, Haluk.The energy spectrum and degeneracy of a Hamiltonian can be studied using either the theory of special functions or spectrum generating algebras. In this thesis the second approach is used for the analysis of the H-atom Hamiltonian. SO(2,1) provides the spectrum generating algebra for the H-atom problem. The geometrical symmetry group SO(3) was rst generalized to SO(4), the degeneracy group, then merging it with SO(2,1), the dynamical group SO(4,2) was obtained. The ladder operators of SO(4,2) connect all the states of the H-atom. In the past, the generators of the SO(2,1) group were generalized by the point transformation r -G(r)^r then these generators are deformed by the variation G(r) - G(r) + g(r). This formalism has led to a perturbation method. In this work the historical development of above formalism is traced and the 15 generators of the SO(4,2) group are deformed.Item Ionization energies of small atoms by momentum space electrostatics(Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.) Ülker, Soydaner.; Beker, Haluk.To calculate ionization energies, a method which uses momentum space techniques for electrostatic problems is described. With this method, a total of fty ve ionization energies of the rst ten elements in the periodic table is calculated and compared with experimental data. Besides, it is examined how violating the Pauli Exclusion Principle a ects the theoretical results of the model. The negligible contributions of the atomic size of the protons and the interactions between intrinsic magnetic dipoles of the particles to the energy calculations are also demonstrated. The necessary underlying calculations used in this study, which may be helpful for future studies, are given in the appendices.Item Uzayda yer tutan magnetik yükler ve bir hadron modeli(Thesis (Assoc. Prof.) - Bogazici University. Institute of Sciences and Engineering, 1977., 1977.) Beker, Haluk.