Ş. Kuru
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SUSY hierarchies of Jaynes–Cummings Hamiltonians with different detuning parameters Open
The aim of this work is to show how supersymmetric (SUSY) quantum mechanics can be applied to the Jaynes–Cummings (JC) Hamiltonian of quantum optics. These SUSY transformations connect pairs of Jaynes–Cummings Hamiltonians characterized by…
The role of the effective mass in two-dimensional Dirac electric quantum dots Open
We investigate the influence of a different effective mass inside and outside an electric quantum dot on in its energy spectrum. Depending on the different values we give to the mass, we have found quite different spectra. Specifically, wh…
Demkov-Fradkin tensor for curved harmonic oscillators Open
In this work, we obtain the Demkov-Fradkin tensor of symmetries for the quantum curved harmonic oscillator in a space with constant curvature given by a parameter $κ$. In order to construct this tensor we have firstly found a set of basic …
Electric and magnetic waveguides in graphene: quantum and classical Open
Electric and magnetic waveguides are considered in planar Dirac materials like graphene as well as their classical version for relativistic particles of zero mass and electric charge. In order to solve the Dirac-Weyl equation analytically,…
SUSY partners and S-matrix poles of the one-dimensional Rosen–Morse II potential Open
Among the list of one-dimensional solvable Hamiltonians, we find the Hamiltonian with the Rosen–Morse II potential. The first objective is to analyse the scattering matrix corresponding to this potential. We show that it includes a series …
Unusual isospectral factorizations of shape invariant Hamiltonians with Scarf II potential Open
In this paper, we search the factorizations of the shape invariant Hamiltonians with Scarf II potential. We find two classes; one of them is the standard real factorization which leads us to a real hierarchy of potentials and their energy …
SUSY partners and $S$-matrix poles of the one dimensional Rosen-Morse II Hamiltonian Open
Among the list of one dimensional solvable Hamiltonians, we find the Hamiltonian with the Rosen--Morse II potential. The first objective is to analyze the scattering matrix corresponding to this potential. We show that it includes a series…
Quantum, classical symmetries and action-angle variables by factorization of superintegrable systems Open
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this proc…
Graphene Dirac fermions in symmetric electric and magnetic fields: the case of an electric square well Open
In this paper, a simple method is proposed to get analytical solutions (or with the help of a finite numerical calculations) of the Dirac-Weyl equation for low energy electrons in graphene in the presence of certain electric and magnetic f…
Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots Open
We study the confinement of Dirac fermions in armchair graphene nanoribbons\nby means of a quantum-dot-type electrostatic potential. With the use of\nspecific projection operators, we find exact solutions for some bound states\nthat satisf…
Dirac-like Hamiltonians associated to Schrödinger factorizations Open
In this work, we have extended the factorization method of scalar shape-invariant Schrö\-din\-ger Hamiltonians to a class of Dirac-like matrix Hamiltonians. The intertwining operators of the Schrödinger equations have been implemented in t…
The solutions of Dirac equation on the hyperboloid under perpendicular magnetic fields Open
In this study, firstly it is reviewed how the solutions of the Dirac-Weyl equation for a massless charge on the hyperboloid under perpendicular magnetic fields are obtained by using supersymmetric (SUSY) quantum mechanics methods. Then, th…
Redundant poles of the $S$-matrix for the one dimensional Morse potential Open
We analyze the structure of the scattering matrix, $S(k)$, for the one dimensional Morse potential. We show that, in addition to a finite number of bound state poles and an infinite number of anti-bound poles, there exist an infinite numbe…
Integrability, Supersymmetry and Coherent States Open
This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics, among them Quantum Optics, Coherent States, Integrable Systems, SUSY Quantum Mechanics, and Mathemat…
Confinement of Dirac electrons in graphene magnetic quantum dots Open
We characterize the confinement of massless Dirac electrons under axially symmetric magnetic fields in graphene, including zero energy modes and higher energy levels. In particular, we analyze in detail the Aharonov-Casher theorem, on the …
Integrals of motion and trajectories for the Perlick system I: an algebraic approach Open
In this paper we tersely recall the main algebraic and geometric properties of the maximally superintegrable system known as "Perlick System Tipe I", considering all possible values of the relevant parameters. We will follow a classical va…
Factorization approach to superintegrable systems: Formalism and applications Open
The factorization technique for superintegrable Hamiltonian systems is\nrevisited and applied in order to obtain additional (higher-order) constants of\nthe motion. In particular, the factorization approach to the classical\nanisotropic os…