42 citations · 311 across the 26 of their papers we have counts for
19 papers · 1 filter
On the exactly-solvable semi-infinite quantum well of the non-rectangular step-harmonic profile
E. I. Jafarov, S. M. Nagiyev
An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum w…
The Krawtchouk oscillator model under the deformed symmetry
E. I. Jafarov, A. M. Jafarova, J. Van der Jeugt
We define a new algebra, which can formally be considered as a deformed Lie algebra. Then, we present a one-dimensional quantum oscillator mod…
On a pair of difference equations for the type orthogonal polynomials and related exactly-solvable quantum systems
E. I. Jafarov, N. I. Stoilova, J. Van der Jeugt
We introduce a pair of novel difference equations, whose solutions are expressed in terms of Racah or Wilson polynomials depending on the nature of the finite-difference step. A nu…
The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials
E. I. Jafarov, J. Van der Jeugt
We investigate an algebraic model for the quantum oscillator based upon the Lie superalgebra sh(2|2), known as the Heisenberg-Weyl superalgebra or "the algebra of supersymmetric qu…
Discrete series representations for sl(2|1), Meixner polynomials and oscillator models
E. I. Jafarov, J. Van der Jeugt
We explore a model for the one-dimensional quantum oscillator based upon the Lie superalgebra sl(2|1). For this purpose, a class of discrete series representations of sl(2|1) is co…
A finite oscillator model related to sl(2|1)
E. I. Jafarov, J. Van der Jeugt
We investigate a new model for the finite one-dimensional quantum oscillator based upon the Lie superalgebra sl(2|1). In this setting, it is natural to present the position and mom…