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Ozlem Yesiltas

Publications and source records attributed to Ozlem Yesiltas.

At least 19 recordsLinked to original sources
arXiv2025

Quantum Particle Creation by Cosmic Strings in de Sitter Spacetime

This paper explores the phenomenon of particle creation associated with cosmic strings in de Sitter spacetime, a model that represents the universe exponential expansion. We examine how the presence of cosmic strings in a de Sitter background affects particle production, focusing on the roles of string tension and angular deficits. Utilizing the Klein Gordon equation adapted to curved spacetime with cosmic string defects, we derive solutions expressed through hypergeometric functions to describe particle states. Our findings highlight how string properties influence particle creation rates and energy distributions. By analyzing both point-like and linear potentials near the string, we determine exact solutions, investigate asymptotic behaviors, and calculate particle creation probabilities using Bogoliubov transformations.

gr-qc↗
arXiv2019

Dirac Equation In The Curved Spacetime and Generalized Uncertainty Principle: A fundamental quantum mechanical approach with energy dependent potentials

In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in a spacetime described by conformally flat metric. Also, supersymmetric quantum mechanics is used both to factorize the Dirac Hamiltonians and obtain new metric functions. Finally, it is observed that the energy dependent potentials may be extended to the energy dependent metric functions.

hep-th↗
arXiv2016

Position Dependent Mass Approach and Quantization for a Torus Lagrangian

We have shown that a Lagrangian for a torus surface can yield second order nonlinear differential equations using the Euler-Lagrange formulation. It is seen that these second order nonlinear differential equations can be transformed into the nonlinear quadratic and Mathews-Lakshmanan equations using the position dependent mass approach developed by Mustafa for the classical systems. Then, we have applied the quantization procedure to the nonlinear quadratic and Mathews-Lakshmanan equations and found their exact solutions.

math-ph↗
arXiv2011

Study of the generalized quantum isotonic nonlinear oscillator potential

We study the generalized quantum isotonic oscillator Hamiltonian given by H=-d^2/dr^2+l(l+1)/r^2+w^2r^2+2g(r^2-a^2)/(r^2+a^2)^2, g>0. Two approaches are explored. A method for finding the quasi-polynomial solutions is presented, and explicit expressions for these polynomials are given, along with the conditions on the potential parameters. By using the asymptotic iteration method we show how the eigenvalues of this Hamiltonian for arbitrary values of the parameters g, w and a may be found to high accuracy.

math-ph↗
arXiv2010

Generalized quantum isotonic nonlinear oscillator in d dimensions

We present a supersymmetric analysis for the d-dimensional Schroedinger equation with the generalized isotonic nonlinear-oscillator potential V(r)={B^2}/{r^{2}}+ω^{2} r^{2}+2g{(r^{2}-a^{2})}/{(r^{2}+a^{2})^{2}}, B\geq 0. We show that the eigenequation for this potential is exactly solvable provided g=2 and (ωa^2)^2 = B^2 +(\ell +(d-2)/2)^2. Under these conditions, we obtain explicit formulae for all the energies and normalized bound-state wavefunctions.

math-ph↗
arXiv2010

Supersymmetric analysis for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions

A supersymmetric analysis is presented for the d-dimensional Dirac equation with central potentials under spin-symmetric (S(r) = V(r)) and pseudo-spin-symmetric (S(r) = - V(r)) regimes. We construct the explicit shift operators that are required to factorize the Dirac Hamiltonian with the Kratzer potential. Exact solutions are provided for both the Coulomb and Kratzer potentials.

math-ph↗
arXiv2010

Comparison theorems for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions

A single Dirac particle is bound in d dimensions by vector V(r) and scalar S(r) central potentials. The spin-symmetric S=V and pseudo-spin-symmetric S = - V cases are studied and it is shown that if two such potentials are ordered V^{(1)} \le V^{(2)}, then corresponding discrete eigenvalues are all similarly ordered E_{κν}^{(1)} \le E_{κν}^{(2)}. This comparison theorem allows us to use envelope theory to generate spectral approximations with the aid of known exact solutions, such as those for Coulombic, harmonic-oscillator, and Kratzer potentials. The example of the log potential V(r) = v\ln(r) is presented. Since $V(r)$ is a convex transformation of the soluble Coulomb potential, this leads to a compact analytical formula for lower-bounds to the discrete spectrum. The resulting ground-state lower-bound curve E_{L}(v) is compared with an accurate graph found by direct numerical integration.

math-ph↗
arXiv2010

The Quantum Effective Mass Hamilton-Jacobi Problem

In this article, the quantum Hamilton- Jacobi theory based on the position dependent mass model is studied. Two effective mass functions having different singularity structures are used to examine the Morse and Poschl- Teller potentials. The residue method is used to obtain the solutions of the quantum effective mass- Hamilton Jacobi equation. Further, it is shown that the eigenstates of the generalized non-Hermitian Swanson Hamiltonian for Morse and Poschl-Teller potentials can be obtained by using the Riccati equation without solving a differential equation.

math-ph↗
arXiv2008

Quantum Hamilton-Jacobi Approach to Two Dimensional Singular Oscillator

We have obtained the solutions of two dimensional singular oscillator which is known as the quantum Calogero-Sutherland model both in cartesian and parabolic coordinates within the framework of quantum Hamilton Jacobi formalism. Solvability conditions and eigenfunctions are obtained by using the singularity structures of quantum momentum functions under some conditions. New potentials are generated by using the first two states of singular oscillator for parabolic coordinates.

quant-ph↗
arXiv2008

Bound state solution of the Schrodinger equation for Mie potential

Exact solution of Schrodinger equation for the Mie potential is obtained for an arbitrary angular momentum. The energy eigenvalues and the corresponding wavefunctions are calculated by the use of the Nikiforov-Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The bound states are calculated numerically for some values of l and $n$ with n<5. They are applied to several diatomic molecules.

quant-ph↗
arXiv2007

A new approach to the exact solutions of the effective mass Schrodinger equation

Effective mass Schrodinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrodinger equation is also solved for the Morse potential transforming to the constant mass Schrödinger equation for a potential. One can also get solution of the effective mass Schrodinger equation starting from the constant mass Schrodinger equation.

quant-ph↗
arXiv2007

Exact Solutions of Schrodinger Equation for a Ring-Shaped Potential

The exact solutions of Schrodinger equation are obtained for a noncentral potential which is a ring-shaped potential. The energy eigenvalues and corresponding eigenfunctions are obtained for any angular momentum l. Nikiforov-Uvarov method is used in the computations.

quant-ph↗
arXiv2006

Exact solutions of Schrodinger equation for PT-/non-PT-symmetric and non-Hermitian Exponential Type Potentials with the position-dependent effective mass

Exact solutions of Schrodinger equation for PT-/non-PT-symmetric and non-Hermitian Morse and Poschl-Teller potentials are obtained with the position-dependent effective mass by applying a point canonical transformation method. Three kinds of mass distributions are used in order to construct exactly solvable target potentials and obtain energy spectrum and corresponding wave functions.

quant-ph↗