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ABSTRACT: By exploring the Position-dependent mass Von Roos Hamiltonian under cylindrical coordinates settings, we discuss the separation of variables of Schrödinger equation. Two radial masses of a coulomb-type and a harmonic oscillator-type are considered, and the effects of various z-dependent interaction potentials on the spectra are studied. Keywords: Power-law potential, Position dependent-masses, cylindrically symmetric settings, exactly solvable models. …………………………………………………………………………………………………………………………
We study the possibility of constructing \ thin-shell wormhole (TSW) in a particular 𝑓����(𝑅����)-gravity model coupled minimally with nonlinear electromagnetic fields. In doing so, first we give a new static spherically symmetric solution of the theory. Then we apply the cut-and-paste method to construct the TSW. As (the third order derivative with respect to 𝑅����) 𝑓����′′′(𝑅����)≠0 we use the specific junction conditions to match the two spacetimes. We find the exact equilibrium radius of the shell from non-black hole solution and show that a linear perturbation leaves the TSW stable. Keywords: 𝑓����(𝑅����) gravity, thin-shell wormhole, junction conditions, non-linear electrodynamics, stability.
ABSTRACT: We study the waves spread in the media, non-linear and non-homogeneous is basic and widespread Problem in physics, which is the subject of our research. We derive the equation of Maxwell for the wave equation based on the z axis and y and find General solutions to the wave equation. We used some of the methods and mathematical processes for the wave equation to be as (hyper-geometric differential equation), and then to be easy to find general solutions to the two parts, the first as a coefficient of permittivity function of y, and the second as a constant. Keywords: Electromagnetics, Permittivity, Permeability. ………………………………………………………………………………………………………………………… ӦZ: Doğrusal ve düzgün (homojen ) olmayan bir ortamda dalgaların yayılma problemi bu tezin özünü oluşturmaktadır. Burada z ve y koordinatlarına bağımlı genel Maxwell denklemleri çözülmüştür. Matematiksel olarak hiper-geometrik difransiyel denklemi elde edilmiş olup onun elektrik geçirgenlik (permitivite) katsayının y – bağımlı ve sabit durumları için çözümler bulunmuştur. Anahtar kelimeler: Elektromagnetizma, Elektrik ve Magnetik geçirgenlik katsayıları.
Global monopoles are topological defects predicted by the Grand Unified Theory throughout the transition phase of the primordial universe. They are formed as a byproduct of spontaneous global symmetry breaking. Their behavior resembles that of the elementary particles with their energies concentrated close to the core of the monopole. They do not have gravitational interactions but they are known to modify spacetime geometry. It is an interesting topic to study Schrödinger particles in a Kratzer Molecular potential in the Global Monopole Spacetime background and under the influence of a Wu-Yang Magnetic Monopole. Some modifications in the spectroscopic structure of such molecular interactions have been observed and reported. This study presents the use of the Schrödinger equation to precisely describe the motion of a particle in the presence of Kratzer potential and a Wu-Yang magnetic monopole. The radial equation was derived and solved to yield the eigenfunctions and eigenvalues for the problem. Keywords: PDM Shrödinger Equation, Point-like Global Monopole, Topological Defect, Kartzer Potential, Wu-Yang Magnetic Monopole.
ABSTRACT: In this thesis we study a quantum particle with position dependent mass (PDM). We start from the general form of the kinetic energy operator in which the physical requirements are considered and then we show that the general form of the kinetic energy operator does not keep the Schrodinger equation invariant under the global Galilean transformation. To make out the problem we introduce instantaneous Galilean invariance and following this concept we show that in some specific case of the general form of the kinetic operator the Schrodinger equation remains invariant under the Galilean transformation. Furthermore we study a specific mass for a particle in an infinite square well potential. We show that the particle prefers to stay in a region with larger mass. Keywords: Position dependent mass, Quantum particle, Galilean invariance, Instantaneous Galilean invariance, Particle in infinite well. …………………………………………………………………………………………………………………………………………………………………………………………………………
ABSTRACT: Reflectance spectroscopy is a method to noninvasively quantitate the scattering and absorption properties of a turbid medium like tissue. The absorption and scattering properties can be used in diagnosis of different diseases such as cancer. Dependence of the acquired spectra to the environmental and physiological factors like probe pressure and habits of the person are being sought out in this thesis. Our applied method, single fiber reflectance (SFR) spectroscopy, uses a single fiber for delivery and detection of the visible light. The SFR spectrum can be fitted by a nonlinear model of the scattering and absorption properties of the tissue under investigation. In this study, SFR measurements are made by a fiber-optic probe gently placed on the lip tissue of some volunteers. The effect of variation in the probe pressure during the measurements is evaluated through the probable change in the extracted parameters from the fitted spectra. In order to do this, first the most appropriate model for the human lip reflectance spectrum is found. Then, the variation in the extracted parameters due to different probe pressures or physiologic characteristics of the volunteers is investigated. Keywords: reflectance spectroscopy - single fiber reflectance spectroscopy. …………………………………………………………………………………………………………………………
Kronig-Penney model is applicable to quantum mechanical study of electrons in confined periodic potentials. Exact solution for a single-well potential can easily be generalized to many-wells through the Bloch theorem. In this study for a single-well potential eigenfunctions/eigenvalues are solvable numerically and forbidden energy gaps are identified. We consider next the potential with double-delta functions for which stationary states and energy levels are found. For this purpose, a transcendental algebraic equation is studied numerically. Reflection and transmission coefficients are determined appropriately. Finally, we propose that the distributional functions must find more applications in quantum mechanical problems.
The Event Horizon Telescope has recently seen the edge of a black hole. This fruitful outcome reveals a fine structure near the black hole horizon. The photon ring and shadow have been clearly observed which provides us with a good opportunity to test general relativity in the regime of strong gravity. In this thesis first we study Schwarzschild black hole and its properties, then we calculate null geodesics of Schwarzschild metric from Euler-Lagrange to find its shadow cast which is two dimensional dark zone in the celestial sphere caused by the strong gravity of the black hole. Last, we study the shadow of the quantum corrected Schwarzschild black hole. Hence, we discuss the effect of the quantum on the shadow of the black hole. Keywords: Gravitation, Black holes, Shadow, Null geodesics, Quantum Corrected Black Holes.
ABSTRACT: In this thesis, self-adjoint extensions of some of the operators used in quantum mechanics are studied. First, the necessary mathematical background namely, the vector spaces and Hilbert space are reviewed. Secondly, the theorem of von-Neumann is introduced to determine the self-adjoint extension of the operators. The application of self-adjoint extensions of the momentum and spatial part of the Klein-Gordon equation is investigated. The concept of quantum singularity structure of the negative mass Schwarzchild spacetime is investigated by the wave obeying the Klein-Gordon equation. Keywords: Self-adjoint extensions, Hilbert-space, von-Neumann Theorem, Klein-Gordon equation. ……………………………………………………………………………………………………………………………………………………………………………………………………………………
In this work, we have used the Friedmann equation of general relativity with quantum correction terms to the Newtonian potential to obtain the modified Friedmann equation with quantum correction. The behavior of the solution is examined with a sign of the correction being put into consideration. With the correction, the singular and non-singular universe is clearly spelled out. The results reveal that the quantum correction effect depends on the sign in the correction. Applying cosmological constant to the modified Friedmann Equation, we found out that the scale factor of the universe is given by the first order in the expression of We also compare the Friedmann Equations with Loop Quantum Gravity (LQG) to the Friedmann Equation with quantum correction and found out that, for negative the critical density is not feasible but it is feasible for positive values . Keywords: Cosmology, quantum cosmology, Cosmological constant, Quantum bounce, Radiation universe, Dust universe.