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 …

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 …

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 …

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 …

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 …

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 …

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) …

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 …

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 …

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-…