Exact solution of the position-dependent effective mass and angular frequency Schrödinger equation: harmonic oscillator model with quantized confinement …
We present an exact solution of a confined model of the non-relativistic quantum harmonic
oscillator, where the effective mass and the angular frequency are dependent on the …
oscillator, where the effective mass and the angular frequency are dependent on the …
The Bannai–Ito algebra and a superintegrable system with reflections on the two-sphere
A quantum superintegrable model with reflections on the two-sphere is introduced. Its two
algebraically independent constants of motion generate a central extension of the Bannai …
algebraically independent constants of motion generate a central extension of the Bannai …
From sl_q (2) to a Parabosonic Hopf Algebra
S Tsujimoto, L Vinet, A Zhedanov - SIGMA. Symmetry, Integrability and …, 2011 - emis.de
A Hopf algebra with four generators among which an involution (reflection) operator, is
introduced. The defining relations involve commutators and anticommutators. The discrete …
introduced. The defining relations involve commutators and anticommutators. The discrete …
The Bannai-Ito algebra and some applications
Abstract The Bannai-Ito algebra is presented together with some of its applications. Its
relations with the Bannai-Ito polynomials, the Racah problem for the sl− 1 (2) algebra, a …
relations with the Bannai-Ito polynomials, the Racah problem for the sl− 1 (2) algebra, a …
Supersymmetric quantum mechanics with reflections
We consider a realization of supersymmetric quantum mechanics where supercharges are
differential-difference operators with reflections. A supersymmetric system with an extended …
differential-difference operators with reflections. A supersymmetric system with an extended …
Bispectrality of the complementary Bannai-Ito polynomials
A one-parameter family of operators that have the complementary Bannai-Ito (CBI)
polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of …
polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of …
Exact quantum-mechanical solution for the one-dimensional harmonic oscillator model asymmetrically confined into the infinite well
EI Jafarov - Physica E: Low-dimensional Systems and …, 2022 - Elsevier
We constructed a new model of the non-relativistic quantum harmonic oscillator within the
canonical approach. It is asymmetrically confined into the infinitely high potential well …
canonical approach. It is asymmetrically confined into the infinitely high potential well …
The Hahn oscillator and a discrete Fourier–Hahn transform
EI Jafarov, NI Stoilova… - Journal of Physics A …, 2011 - iopscience.iop.org
We define the quadratic algebra $\mathfrak {su}(2) _\alpha $ which is a one-parameter
deformation of the Lie algebra $\mathfrak {su}(2) $ extended by a parity operator. The odd …
deformation of the Lie algebra $\mathfrak {su}(2) $ extended by a parity operator. The odd …
Integrated optical wave analyzer using the discrete fractional Fourier transform
Within the expansive domain of optical sciences, achieving the precise characterization of
light beams stands as a fundamental pursuit, pivotal for various applications, including …
light beams stands as a fundamental pursuit, pivotal for various applications, including …
Dual-1 Hahn polynomials:“classical” polynomials beyond the Leonard duality
S Tsujimoto, L Vinet, A Zhedanov - Proceedings of the American …, 2013 - ams.org
We introduce the $-$1 dual Hahn polynomials through an appropriate $ q\to-1$ limit of the
dual $ q $-Hahn polynomials. These polynomials are orthogonal on a finite set of discrete …
dual $ q $-Hahn polynomials. These polynomials are orthogonal on a finite set of discrete …