arXiv subjects

O. Yesiltas

Publications and source records attributed to O. Yesiltas.

5 recordsLinked to original sources

arXiv2024

Supersymmetric Analysis of Spinning Cosmic String Spacetime Within External fields with Aharonov-Bohm interaction

The supersymmetric analysis of spinning cosmic string spacetime, involving an electron in magnetic fields, has been conducted. We examined the Dirac system within extended special functions known as exceptional orthogonal polynomials. Corresponding Dirac system is transformed to a relativistic system with a nonlinear isotonic oscillator. Furthermore, new potential models that extend the radial oscillator by adding rational terms are expressed in terms of the exceptional orthogonal Laguerre $X_{m}$ polynomial. The necessary analyses of the potential, energy levels, and probability density graphs are introduced for various cosmic string topological defects and Aharonov-Bohm interaction parameters.

math-ph↗

arXiv2020

The extension of the massless fermion in the cosmic string spacetime

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 an extension of these three potential models and their solutions are also obtained. The energy spectrum and potential graphs for each case are discussed for the $α$ deficit angle.

hep-th↗

arXiv2017

The massless Dirac-Weyl equation with deformed extended complex potentials

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. Moreover, the Lie algebraic analysis is performed.

math-ph↗

arXiv2013

$su(1,1)\simeq so(2,1)$ Lie Algebraic Extensions of the Mie-type Interactions with Positive Constant Curvature

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 operators, we have given the generators of $so(2,1)$ algebra and the Casimir operator which are related to the Mie Oscillator on the positive curvature.

math-ph↗

arXiv2013

$\mathcal{PT}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions

In this article, we have introduced a $\mathcal{PT}$ symmetric non-Hermitian Hamiltonian model which is given as $\hat{\mathcal{H}}=ω(\hat{b}^†\hat{b}+1/2)+ α(\hat{b}^{2}-(\hat{b}^†)^{2})$ where $ω$ and $α$ are real constants, $\hat{b}$ and $\hat{b^†}$ are first order differential operators. The Hermitian form of the Hamiltonian $\mathcal{\hat{H}}$ is obtained by suitable mappings and it is interrelated to the time independent one dimensional Dirac equation in the presence of position dependent mass. Then, Dirac equation is reduced to a Schrödinger-like equation and two new complex non-$\mathcal{PT}$ symmetric vector potentials are generated. We have obtained real spectrum for these new complex vector potentials using shape invariance method. We have searched the real energy values using numerical methods for the specific values of the parameters.

math-ph↗