User profiles for author:Atakishiyev Natig
Natig M. AtakishiyevProfessor of Instituto de Matemáticas, UNAM, Unidad Cuernavaca Verified email at matcuer.unam.mx Cited by 2822 |
Fractional fourier–kravchuk transform
NM Atakishiyev, KB Wolf - JOSA A, 1997 - opg.optica.org
We introduce a model of multimodal waveguides with a finite number of sensor points. This
is a finite oscillator whose eigenstates are Kravchuk functions, which are orthonormal on a …
is a finite oscillator whose eigenstates are Kravchuk functions, which are orthonormal on a …
Finite two-dimensional oscillator: I. The Cartesian model
NM Atakishiyev, GS Pogosyan… - Journal of Physics A …, 2001 - iopscience.iop.org
A finite two-dimensional oscillator is built as the direct product of two finite one-dimensional
oscillators, using the dynamical Lie algebra su (2) x⊕ su (2) y. The position space in this …
oscillators, using the dynamical Lie algebra su (2) x⊕ su (2) y. The position space in this …
Wigner distribution function for finite systems
NM Atakishiyev, SM Chumakov, KB Wolf - Journal of Mathematical …, 1998 - pubs.aip.org
We construct a Wigner distribution function for finite data sets. It is based on a finite optical
system; a linear wave guide where the finite number of discrete sensors is equal to the …
system; a linear wave guide where the finite number of discrete sensors is equal to the …
[HTML][HTML] Continuous vs. discrete fractional Fourier transforms
NM Atakishiyev, LE Vicent, KB Wolf - Journal of computational and applied …, 1999 - Elsevier
We compare the finite Fourier (-exponential) and Fourier–Kravchuk transforms; both are
discrete, finite versions of the Fourier integral transform. The latter is a canonical transform …
discrete, finite versions of the Fourier integral transform. The latter is a canonical transform …
Meixner oscillators
Meixner oscillators have a ground state and an `energy' spectrum that is equally spaced;
they are a two-parameter family of models that satisfy a Hamiltonian equation with a {\it …
they are a two-parameter family of models that satisfy a Hamiltonian equation with a {\it …
The Wigner function for general Lie groups and the wavelet transform
ST Ali, NM Atakishiyev, SM Chumakov, KB Wolf - Annales Henri Poincaré, 2000 - Springer
We build Wigner maps, functions and operators on general phase spaces arising from a
class of Lie groups, including non-unimodular groups (such as the affine group). The phase …
class of Lie groups, including non-unimodular groups (such as the affine group). The phase …
Wigner distribution function for Euclidean systems
LM Nieto, NM Atakishiyev… - Journal of Physics A …, 1998 - iopscience.iop.org
Euclidean systems include poly-and monochromatic wide-angle optics, acoustics, and also
infinite discrete data sets. We use a recently defined Wigner operator and (quasiprobability) …
infinite discrete data sets. We use a recently defined Wigner operator and (quasiprobability) …
Contraction of the finite one-dimensional oscillator
NM Atakishiyev, GS Pogosyan… - International Journal of …, 2003 - World Scientific
The finite oscillator model of 2j + 1 points has the dynamical algebra u(2), consisting of
position, momentum and mode number. It is a paradigm of finite quantum mechanics where a …
position, momentum and mode number. It is a paradigm of finite quantum mechanics where a …
Quantum algebraic structures compatible with the harmonic oscillator Newton equation
We study some of the algebraic structures that are compatible with the quantization of the
harmonic oscillator through its Newton equation. Examples of such structures are given; they …
harmonic oscillator through its Newton equation. Examples of such structures are given; they …
A simple difference realization of the Heisenberg q‐algebra
A realization of the Heisenberg q-algebra whose generators are first-order difference
operators on the full real line is discussed herein. The eigenfunctions of the corresponding q-…
operators on the full real line is discussed herein. The eigenfunctions of the corresponding q-…