Browsing by Author "Erkol, Hakan."

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    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.
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    Exactly solvable potentials with Dirac delta point interactions
    (Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009., 2009.) Erkol, Hakan.; Demiralp, Ersan.
    A general method to obtain s-wave bound states of the Schrödinger equation for analytically solvable potentials together with a finite number of the Dirac delta functions is presented for three-dimensional systems. The eigenvalue equations for the finite number of the Dirac delta decorated Woods-Saxon potential and Morse potential are obtained and the eigenvalue equations are calculated numerically for one Dirac delta function. The eigenvalue equation is solved numerically for two delta function case for the Woods-Saxon potential. The change of the ground state energies as a function of strength and locations of the Dirac delta functions are investigated for these potentials. For a hydrogen molecule, which is described by the Morse potential, transition probabilities between the initial state of the Hamiltonian and the final state of the perturbed Hamiltonian for a sudden, very local perturbation are calculated. The conditions for the number of bound states for given parameters of the Woods-Saxon and the Morse potentials are analyzed. Our results for the Woods-Saxon potential can be used to model very short range interactions for atomic and nuclear systems. Our method is applied to hydrogen molecule, which is described by the Morse potential, in C60 fullerene cage and the stabilization energy is calculated by representing the interaction potential between H2 and C60 by the Dirac delta interaction. Interatomic interactions that are described by the Morse potential together with local deformations can be investigated by using our model.
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    The ultrasonic properties of colon cancer tissue
    (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2020., 2020.) Yelken, Şerife Züleyha.; Erkol, Hakan.
    Cancer is the most threatening disease for human life. Therefore, diagnosis of cancer is very important. For cancer diagnosis, many medical imaging systems have been developed. Ultrasonic imaging is one of them. Colon cancer presents a significant important statistics amongst all cancer types. Colon cancer is the third most common cancer diagnosed in all cancer cases. Both diagnosis of colon cancers and determining tumor limits precisely are quite important for patients’ lives and life quality. In this thesis, healthy and tumorous colon tissues from 3 different patients are examined by using Scanning Acoustic Microscopy. Ultrasonic properties of those tissues are presented. The difference of ultrasonic properties between healthy and tumorous colon tissues is observed. For a better determination of the tumor, a new computer program is developed providing detailed images and analysis tool.