相关论文: $SU(1,1)$ solution for the Dunkl oscillator in two…
We study the radial part of the Dunkl-Coulomb problem in two dimensions and show that this problem possesses the $su(1,1)$ symmetry. We introduce two different realizations for the $su(1,1)$ Lie algebra and use the theory of irreducible…
We decouple the Dirac's radial equations in $D+1$ dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an…
We study some properties of the $SU(1,1)$ Perelomov number coherent states. The Schr\"odinger's uncertainty relationship is evaluated for a position and momentum-like operators (constructed from the Lie algebra generators) in these number…
We apply the Schr\"odinger factorization method to the radial second-order equation for the relativistic Kepler-Coulomb problem. From these operators we construct two sets of one-variable radial operators which are realizations for the…
We introduce an $SU(1,1)$ algebraic approach to study the $(2+1)$-Dirac oscillator in the presence of the Aharonov-Casher effect coupled to an external electromagnetic field in the Minkowski spacetime and the cosmic string spacetime. This…
Using representation-theoretic techniques associated with the $\mathfrak{su}(1,1)$ symmetry algebra, we construct Perelomov coherent states for the Dunkl-Klein-Gordon equation in its canonical form, which is free of first-order Dunkl…
The isotropic Dunkl oscillator model in three-dimensional Euclidean space is considered. The system is shown to be maximally superintegrable and its symmetries are obtained by the Schwinger construction using the raising/lowering operators…
We study the Dirac equation with Coulomb-type vector and scalar potentials in D + 1 dimensions from an su(1, 1) algebraic approach. The generators of this algebra are constructed by using the Schr\"odinger factorization. The theory of…
We show that the $(2+1)$-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field can be treated algebraically with the $SU(1,1)$ group theory and its group basis. We use the $su(1,1)$ irreducible representation theory…
We construct the Perelomov number coherent states for any three $su(1,1)$ Lie algebra generators and study some of their properties. We introduce three operators which act on Perelomov number coherent states and close the $su(1,1)$ Lie…
We apply the Schr\"odinger factorization to construct the ladder operators for hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the…
In this paper we study a two-dimensional [2D] rotationally symmetric harmonic oscillator with time-dependent frictional force. At the classical level, we solve the equations of motion for a particular case of the time-dependent coefficient…
In this article we investigate and solve exactly the modified Dirac oscillator in curved spacetime with spin and pseudospin symmetries through an algebraic approach. By focusing on the radial part of this problem, we use the Schr\"odinger…
We study the Dunkl anharmonic oscillator (Kerr medium) Hamiltonian from an algebraic approach of the $SU(1,1)$ group. In order to obtain the exact energy spectrum of this problem, we write its Hamiltonian in terms of the Dunkl creation and…
We study the parametric amplifier Hamiltonian within the framework of the Dunkl formalism. We introduce the Dunkl creation and annihilation operators and show that their quadratic combinations generate an $su(1,1)$ Lie algebra. The spectral…
We present exact solutions of the Dirac equation in static curved space-time using two distinct algebraic approaches. The first method employs $su(1,1)$ algebra operators together with the tilting transformation, enabling the derivation of…
The bound-state solutions and the su(1,1) description of the $d$-dimensional radial harmonic oscillator, the Morse and the $D$-dimensional radial Coulomb Schr\"odinger equations are reviewed in a unified way using the point canonical…
Two Dunkl oscillator models are considered: one singular and the other with a 2:1 frequency ratio. These models are defined by Hamiltonians which include the reflection operators in the two variables x and y. The singular or caged Dunkl…
The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a Hamiltonian constructed from the combination of two independent parabosonic oscillators. The system is superintegrable and its symmetry generators…
In this paper we study the $(2+1)$-dimensional Dirac-Dunkl oscillator coupled to an external magnetic field. Our Hamiltonian is obtained from the standard Dirac oscillator coupled to an external magnetic field by changing the partial…