14 citations · 38 across the 15 of their papers we have counts for
15 papers
Calculating the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials
V. V. Borzov, E. V. Damaskinsky
In this paper, we calculate the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials \cite{01}, \cite{02}, \cite{03}. The sign of the…
Realization by a differential operator of the annihilation operator for generalized Chebyshev oscillator
V. V. Borzov, E. V. Damaskinsky
We study a generalized Chebyshev oscillator [1] associated with a point interaction for the discrete Schrödinger equation. Our goal is to find a realization of the annihilation ope…
On the spectrum of discrete Schrödinger equation with one-dimensional perturbation
V. V. Borzov, E. V. Damaskinsky
We consider the spectrum of the discrete Schrödinger equation with one-dimensional perturbation. We obtain the explicit form of scattering matrix and find the exact condition of ab…
Invariance of the generalized oscillator under linear transformation of the related system of orthogonal polynomials
V. V. Borzov, E. V. Damaskinsky
We consider two families of polynomials $\mathbb{P}=\polP$ and $\mathbb{Q}=\polQ$\footnote{Here and below we consider only monic polynomials.} orthogonal on the real line with resp…
Comment on "On the dimensions of the oscillator algebras induced by orthogonal polynomials" [J. Math. Phys. {\bf 55}, 093511 (2014)]
V. V. Borzov, E. V. Damaskinsky
In the interesting paper G. Honnouvo and K. Thirulogasanthar [J. Math. Phys. {\bf 55} , 093511 (2014)] the authors obtained the necessary and sufficient conditions under which the…
Orthogonal polynomials and deformed oscillators
V. V. Borzov, E. V. Damaskinsky
We discuss the construction of oscillator-like systems associated with orthogonal polynomials on the example of the Fibonacci oscillator. In addition, we consider the dimension of…