Özlem YeşiltaşGazi University · Department of Physics
Özlem Yeşiltaş
PhD
About
60
Publications
6,420
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532
Citations
Introduction
*Quantum Gravity
*Relativistic Quantum Mechanics
*Special Functions of Mathematical Physics
*Supersymmetric Quantum Mechanics
*PT Symmetric & Pseudo-Hermitian Quantum Mechanics
Skills and Expertise
Publications
Publications (60)
In this work, we explore the strain and curvature effects on the electronic properties of a curved graphene structure, called the graphene wormhole. The electron dynamics is described by a massless Dirac fermion containing position-dependent Fermi velocity. In addition, the strain produces a pseudo-magnetic vector potential to the geometric couplin...
We have discussed the Dirac equation in Schwarzschild spacetime using pseudo-supersymmetric quantum mechanics and have obtained the partner Hamiltonian of the initial Hamiltonian operator. We demonstrate that the partner metric tensors, corresponding to these Hamiltonians, can be derived using the intertwining relations inherent in pseudo-supersymm...
In this work, we explore the strain and curvature effects on the electronic properties of a curved graphene structure, called the graphene wormhole. The electron dynamics is described by a massless Dirac fermion containing position--dependent Fermi velocity. In addition, the strain produces a pseudo--magnetic vector potential to the geometric coupl...
In this paper, we have presented the Dirac equation in the frame of position-dependent mass on two dimensional gravitational background in the presence of PT /non-PT -symmetric potential interactions. We have obtained the eigenvalues of the Dirac operator for the complex Morse and trigonometric complex Scarf-II potentials SL(2, C) Lie algebras and...
The Dirac equation in (2+1) dimensions on the toroidal surface is studied for a massless fermion particle under the action of external fields. Using the covariant approach based on general relativity, the Dirac operator stemming from a metric related to the strain tensor is discussed within the pseudo-Hermitian operator theory. Furthermore, analyti...
In this paper, we study the Dirac equation for an electron constrained to move on a catenoid surface. We decoupled the two components of the spinor and obtained two Klein-Gordon-like equations. Analytical solutions were obtained using supersymetric quantum mechanics for two cases, namely the constant Fermi velocity and the position-dependent Fermi...
We have generalized the solutions of the radial Dirac equation with a tensor potential under spin and pseudospin symmetry limits to exceptional orthogonal Hermite polynomials family. We have obtained new general rational potential models which are the generalization of the nonlinear isotonic potential families and also energy dependent.
The Dirac equation in $(2+1)$ dimensions on the toroidal surface is studied for a massless fermion particle under the action of external fields. Using the covariant approach based on general relativity, the Dirac operator stemming from a metric related to the strain tensor is discussed within the Pseudo-Hermitian operator theory. Furthermore, analy...
We have generalized the solutions of the radial Dirac equation with a tensor potential under spin and pseudospin symmetry limits to exceptional orthogonal Hermite polynomials family. We have obtained new general rational potential models which are the generalization of the nonlinear isotonic potential families and also energy dependent.
In this paper, we study the Dirac equation for an electron constrained to move on a catenoid surface. We decoupled the two components of the spinor and obtained two Klein-Gordon-like equations. Analytical solutions were obtained using supersymmetric quantum mechanics for two cases, namely, the constant Fermi velocity and the position-dependent Ferm...
In this work, we have obtained the solutions of a massless fermion which is under the external magnetic field around a cosmic string for specific three potential models using supersymmetric quantum mechanics. The constant magnetic field, energy-dependent potentials, and position-dependent mass models are investigated for the Dirac Hamiltonians, and...
In this work, we have obtained the solutions of a massless fermion which is under the external magnetic field around a cosmic string for specific three potential models using supersymmetric quantum mechanics. The constant magnetic field, energy dependent potentials and position dependent mass models are investigated for the Dirac Hamiltonians and a...
This work is based on deploying the algorithm of the second-order supersymmetric quantum mechanics to the spin \(\frac{1}{2}\) particle behavior in a cosmic sting spacetime. The spectral equivalence of the different systems may shed a light on the quantum mechanics for the topological defects. From this point of view, we have obtained the solutions...
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 fact...
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 fact...
The quantum mechanical formalism for systems featuring energy-dependent potentials is extended to systems governed by generalized Schrödinger equations that include the position-dependent mass case. Modified versions of the probability density and the probability current lead to adjustments in the scalar product and the norm. Our results are applie...
Basically (2 + 1)-dimensional Dirac equation with real deformed Lorentz scalar potential is investigated in this study. The position-dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein–Gordon-like effective Hamiltonian system. The complex Hamiltonian and its real energy spectrum and eigenvectors are obtained analytically. Mo...
We extend the confluent version of the higher-order supersymmetry (SUSY) formalism to general linear differential equations of second order. Closed-form representations of transformation functions, their Wronskians, and of the general solutions to SUSY-transformed equations are derived. We use these results to construct formulas for resolving multi...
The exact solutions of the (2+1) dimensional Dirac equation on the torus and the new extension and generalization of the trigonometric Poschl-Teller potential families in terms of the torus parameters are obtained. Supersymmetric quantum mechanical techniques are used to get the extended potentials when the inner and outer radii of the torus are bo...
We present closed-form solutions of the two-dimensional massless Dirac equation for hyperbolic potentials that are rationally extended in terms of \( X_{m}\)-Jacobi polynomials. Our method of construction is based on rational extensions of nonrelativistic Scarf and Pöschl-Teller models that include \( {PT}\)-symmetric and energy-dependent cases.
Basically (2 + 1) dimensional Dirac equation with real deformed Lorentz scalar potential is investi gated in this study. The position dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein-Gordon-like effective Hamiltonian system. The complex Hamiltonian and its real energy spectrum and eigenvectors are obtained analytically. M...
The Dirac equation on the toroidal surface is studied. The non-constant Fermi velocity functions are used in the Dirac Hamiltonian to get trigonometric Scarf and Rosen-Morse potentials using the method given in [19], then, the exact solutions are written. On the other hand, consecutive mappings are used to get a trigonometric Scarf I-like potential...
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...
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...
We have studied a relativistic electron in the presence of a uniform magnetic
field and scalar potential in the cosmic string spacetime. The exact solutions
of the Dirac equation with a Coulomb-like scalar potential and linear vector
potential through the gravitational fields are found using SU(1,1) Lie
algebras.
We have studied a relativistic electron in the presence of a uniform magnetic field and scalar potential in the cosmic string spacetime. The exact solutions of the Dirac equation with a Coulomb-like scalar potential and linear vector potential through the gravitational fields are found using $ SU(1,1)$ Lie algebras. © 2015, Società Italiana di Fisi...
The Dirac Hamiltonian in the (2+1) dimensional curved space-time has been
studied with a metric for an expanding de Sitter space-time which is a two
sphere. The spectrum and the exact solutions of the time dependent
non-Hermitian and angle dependent Hamiltonians are obtained in terms of the
Jacobi and Romanovski polynomials. Hermitian equivalent of...
The Dirac equation in (1 + 1) dimension with the complex vector potential coupling that leads to an effective Hulthen potential model is solved. Polynomial solutions are obtained using the method of Nikiforov-Uvarov. Energy spectrum and corresponding wave-functions are obtained.
Two-dimensional massless Dirac Hamiltonian under the influence of hyperbolic magnetic fields is mentioned in curved space. Using a spherical surface parameterization, the Dirac operator on the sphere is presented and the system is given as two supersymmetric partner Hamiltonians which coincides with the position dependent mass Hamiltonians. We intr...
Two dimensional effective Hamiltonian for a massless Dirac electron
interacting with a hyperbolic magnetic ?eld is discussed within PT symmetry.
Factorization method and polynomial procedures are used to solve Dirac equation
for the constant Fermi velocity and the effective potential which is complex
Scarf II potential. The more general effective S...
In this paper, we have provided a matrix Hamiltonian model for honeycomb lattices and subsequently obtained the dispersion relation. Furthermore, we have constructed the C operator for the given non-Hermitian Hamiltonian model. The quadratic surfaces are sketched and the quantum Brachistochrone problem is discussed for the given honeycomb lattice m...
We have obtained the metric operator 2 = exp T for the non-Hermitian Hamiltonian model
H = !(a†a + 1/2) + �(a2 −a†2
). We also found the intertwining operator that connects the
Hamiltonian to the adjoint of its pseudo-super-symmetric partner Hamiltonian for the model
of the hyperbolic Rosen–Morse II potential.
In this article, we have introduced a $\mathcal{PT}$ symmetric non-Hermitian
Hamiltonian model which is given as $\hat{\mathcal{H}}=\omega
(\hat{b}^{\dag}\hat{b}+1/2)+ \alpha (\hat{b}^{2}-(\hat{b}^{\dag})^{2})$ where
$\omega$ and $\alpha$ are real constants, $\hat{b}$ and $\hat{b^{\dag}}$ are
first order differential operators. The Hermitian form o...
The Schrödinger equation in three-dimensional space with constant positive curvature is studied for the Mie potential. Using analytic polynomial solutions, we have obtained whole spectrum of the corresponding system. With the aid of factorization method, ladder operators are obtained within the variable and function transformations. Using ladder op...
In this paper, we have introduced a symmetric non-Hermitian Hamiltonian model which is given as where ω and α are real constants, and are first-order differential operators. The Hermitian form of the Hamiltonian is obtained by suitable mappings and it is interrelated to the time-independent one-dimensional Dirac equation in the presence of position...
Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian
Hamiltonian $H_{-}=\omega(\xi^{\dag} \xi+\1/2)+\alpha \xi^{2}+\beta \xi^{\dag
2}$, where $\alpha \neq \beta$ and $\xi$ is a first order differential
operator, to obtain the partner potentials $V_{+}(x)$ and $V_{-}(x)$ which are
new isotonic and isotonic nonlinear oscillators,...
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...
We present a supersymmetric analysis for the d-dimensional Schroedinger
equation with the generalized isotonic nonlinear-oscillator potential
V(r)={B^2}/{r^{2}}+\omega^{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 (\omega a^2)^2 = B^2 +(\ell +(d-2)/2)...
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...
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_{\kappa \nu}^{(1)} \le E_{\kap...
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. Furt...
We present a variational approach to a general Lienard-type equation in order
to linearize it and, as an example, the Van der Pol oscillator is discussed.
The new equation which is almost linear is factorized. The point symmetries of
the deformed equation are also discussed and the two-dimensional Lie algebraic
generators are obtained.
A general form of the effective mass Schrödinger equation is solved exactly for Hulthen 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.
We have constructed the quasi-exactly-solvable two-mode bosonic realization of SU(2). Two-mode boson Hamiltonian is defined through a differential equation which is solved by quantum Hamilton-Jacobi formalism.
The squeezed states of two-mode boson systems are characterized through canonical transformation. The illustrated concept
of squeezed boson...
Effective mass Schrödinger 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 Schrödinger equation is also solved for the Morse potential transforming to the consta...
We obtain 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 s...
We show that a wide class of non-central potentials can be analysed via the improved picture of the Nikiforov–Uvarov method [Physica Scripta 75 (2007) 686]. It has been shown that using the alternative approach, polynomial solutions of three-dimensional separable non-central potential can be obtained.
PT-/non-PT-symmetric and non-Hermitian deformed Morse and Pöschl-Teller potentials are studied first time by quantum Hamilton–Jacobi
approach. Energy eigenvalues and eigenfunctions are obtained by solving quantum Hamilton–Jacobi equation.
The generalized Sinh-Gordon potential is solved within quantum Hamiltonian Jacobi approach in the framework of PT symmetry. The quasi exact solutions of energy eigenvalues and eigenfunctions of the generalized Sinh-Gordon potential are
found for n=0,1 states.
Exact solution of Schrödinger 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...
Exact solution of Schrödinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The
energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov–Uvarov method. Wavefunctions are expressed
in terms of Jacobi polynomials. The energy eigenvalues are calculated numerically for some values of ℓ a...
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...
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 consta...
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.
The solutions of trigonometric Scarf potential, PT/non-PT symmetric and non-Hermitian q-deformed hyperbolic Scarf and Manning–Rosen potentials are obtained by solving the Schrödinger equation. The Nikiforov–Uvarov method is used to obtain the real energy spectra and corresponding eigenfunctions.
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
spect...
In this study, we use perturbation approximations and semiclassical
methods to investigate the boundary solutions of non-linear vibrating
systems. The extended Mathieu Equation, related to the perturbed Van der
Pol oscillator with periodic coefficients, is solved using multiple time
scales. Then, using the Von Zeipel Method, which is based on the
H...
Using the NU method [A.F.Nikiforov, V.B.Uvarov, Special Functions of Mathematical Physics, Birkhauser,Basel,1988], we investigated the real eigenvalues of the complex and/or $PT$- symmetric, non-Hermitian and the exponential type systems, such as Poschl-Teller and Morse potentials. Comment: 14 pages, Latex
Questions
Question (1)
Dear Colleague,
We invite you to our international conference titled “Approximation Theory and Special Functions - ATSF Conference - 8th Series”. There will be a special mathematical physics session too.
I would like to briefly inform you about the history of the ATSF organization. ATSF is an international conference series that brings together all researchers in the field of Approximation Theory and Special Functions to discuss new ideas and new applications. This organization, which has been organized seven times as mini-symposia in various European countries, has gradually grown over the years, resulting in the need for an international conference.
The ATSF series we have organized so far are as follows:
· the 1st series in Greece in 2013 (as a part of the ICNAAM 2013 Conference)
· the 2nd series in Bulgaria in 2014 (as a part of the MDS 2014 Conference)
· the 3rd series in France in 2016 (as a part of the ETAMM 2016 Conference)
· the 4th series in Sweden in 2017 (as a part of the ISAAC 2017 Conference)
· the 5th series in Hungary in 2018 (as a part of the ICPAM 2018 Conference)
· the 6th series in Belgium in 2019 (as a part of the ICPAM 2019 Conference)
· the 7th series in Turkey in 2020 (as a part of the ICRAPAM 2020 Conference)
Our 6th series, held in Belgium, was awarded the “Best Organization Award” by the IEEE ICMAE Organization. Moreover, the presentations in the 5th and 6th series of ATSF won the “Best Presentation Award” at the ICPAM conferences. We are coming together again in 2024 with a big organization for our conference series, which we had to take a break due to the pandemic that affected the whole world between 2020-2022 and the earthquake disaster that occurred in Turkey in February 2023. This time, we have tried to keep the conference research and presentation topics as broad as possible. In addition to paper presentations, we will also welcome poster presentations and special session proposals. So, we expect a big turnout for this series.
The eighth series of the ATSF Conference will be hosted by TOBB Economics and Technology University (Ankara, Türkiye) on September 4-7, 2024.
Our conference web page: https://sites.google.com/view/atsf2024
We invite you to meet leading mathematicians, researchers, and academics from around the world at this conference, to benefit from their experiences and knowledge, and to enrich your own perspective. This event will be a meeting point for anyone interested in mathematics, so we welcome participants of all levels.
International advisory and scientific committee and invited speakers of the ATSF 2024 Conference are distinguished scientists in the field. Please visit the conference web page for all details (see also the “special session” titles approved so far).
The international publishers and journals that have so far agreed to publish the conference proceedings as a special volume/issue are listed below (this list will be updated over time):
· Springer Proceedings in Mathematics & Statistics (indexed by ISI Web of Science, Scopus, and AMS Mathematical Reviews).
· Demonstratio Mathematica (indexed by ISI Web of Science, Science Citation Index - Q1, Scopus - Q1, and AMS Mathematical Reviews).
· Dolomites Research Notes on Approximation (indexed by ISI Web of Science, Emerging Source Citation Index, Scopus, and AMS Mathematical Reviews)
The topics we will focus on at the conference are (but of course not limited to) the following:
· Approximation Theory: Classical approximation, statistical approximation, fuzzy approximation, approximation in the complex plane, best approximation, interpolation, linear and nonlinear approximation, multivariate approximation, neural network approximation, numerical approximation, rational approximation, ... and their applications.
· Summability Theory: Statistical convergence, regular summability methods, power series methods, sequence spaces, divergent series, Tauberian theorems, summation process, matrix and integral methods for summability, ... and their applications.
· Applied Mathematics: Ordinary differential equations, partial differential equations, difference equations, mathematical modeling, dynamical systems, numerical analysis, oscillation and stability theory, control theory, financial mathematics, probability and statistics, stochastic processes, graph theory, ... and their applications.
· Special Functions: Orthogonal polynomials, hypergeometric series, generating functions, general orthogonal systems, umbral calculus, recurrence relations, matrix-valued polynomials, Fourier series, special orthogonal functions, special polynomials, special functions in mathematical physics,... and their applications.
· Analysis and Functions Theory: Harmonic analysis, functional analysis, fuzzy logic theory, operator theory, spectral theory, fixed point theory, fractional derivative, q-analysis, number theory, inequalities, time scales, ... and their applications.
The web page of the ATSF 2024 Conference is announced on the following platforms:
· American Mathematical Society
· European Mathematical Society
For all inquiries regarding the conference, please contact atsf2024@gmail.com and yesiltas@gazi.edu.tr
See you in September 2024!
Prof. Dr. Özlem Yeşiltaş
