Classical and quantum superintegrability with applications

W Miller, S Post, P Winternitz - Journal of Physics A: Mathematical …, 2013 - iopscience.iop.org
A superintegrable system is, roughly speaking, a system that allows more integrals of motion
than degrees of freedom. This review is devoted to finite dimensional classical and quantum …

[图书][B] Orthogonal polynomials of several variables

CF Dunkl, Y Xu - 2014 - books.google.com
Serving both as an introduction to the subject and as a reference, this book presents the
theory in elegant form and with modern concepts and notation. It covers the general theory …

The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic

B Hamil, BC Lütfüoğlu - Physica A: Statistical Mechanics and its …, 2023 - Elsevier
In the framework of the theory of Dunkl-deformed bosons, Bose–Einstein condensation of
two and three-dimensional Dunkl-boson gases confined in the one-dimensional …

Thermal properties of relativistic Dunkl oscillators

B Hamil, BC Lütfüoğlu - The European Physical Journal Plus, 2022 - Springer
For a better understanding of the physical systems, even at the quantum level, the thermal
quantities can be investigated. Recently, we realized that the parity of the system can also …

Ideal Bose gas and blackbody radiation in the Dunkl formalism

F Merabtine, B Hamil, BC Lütfüoğlu… - Journal of Statistical …, 2023 - iopscience.iop.org
Recently, deformed quantum systems have received lots of attention in the literature. Dunkl
formalism differs from others by containing the difference-differential and reflection operator …

Exact solutions of the 2D Dunkl–Klein–Gordon equation: The Coulomb potential and the Klein–Gordon oscillator

RD Mota, D Ojeda-Guillén… - … Physics Letters A, 2021 - World Scientific
We introduce the Dunkl–Klein–Gordon (DKG) equation in 2D by changing the standard
partial derivatives by the Dunkl derivatives in the standard Klein–Gordon (KG) equation. We …

One-dimensional quantum mechanics with Dunkl derivative

WS Chung, H Hassanabadi - Modern Physics Letters A, 2019 - World Scientific
In this paper, we consider the quantum mechanics with Dunkl derivative. We use the Dunkl
derivative to obtain the coordinate representation of the momentum operator and …

The Dunkl oscillator in the plane II: representations of the symmetry algebra

VX Genest, MEH Ismail, L Vinet, A Zhedanov - … in Mathematical Physics, 2014 - Springer
The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model
in the plane were considered in the first part. Here finite-dimensional representations of the …

Coherent states of the one-dimensional Dunkl oscillator for real and complex variables and the Segal–Bargmann transformation of Dunkl-type

S Ghazouani - Journal of Physics A: Mathematical and …, 2023 - iopscience.iop.org
In this paper, we construct coherent states of a parity deformation of the Heisenberg algebra
and we examine some of its properties. We show that these states minimize the uncertainty …

Dunkl graphene in constant magnetic field

B Hamil, BC Lütfüoğlu - The European Physical Journal Plus, 2022 - Springer
Graphene-based materials are thought to revolutionize entire industries. Therefore, many
researches are being carried on graphene theoretically and experimentally. On the other …