Meixner Oscillators
Abstract
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 difference} operator. Meixner oscillators include as limits and particular cases the Charlier, Kravchuk and Hermite (common quantum-mechanical) harmonic oscillators. By the Sommerfeld-Watson transformation they are also related with a relativistic model of the linear harmonic oscillator, built in terms of the Meixner-Pollaczek polynomials, and their continuous weight function. We construct explicitly the corresponding coherent states with the dynamical symmetry group Sp(2,). The reproducing kernel for the wavefunctions of these models is also found.
Cite
@article{arxiv.math-ph/9807035,
title = {Meixner Oscillators},
author = {Natig M. Atakishiyev and Elchin I. Jafarov and Shakir M. Nagiev and Kurt B. Wolf},
journal= {arXiv preprint arXiv:math-ph/9807035},
year = {2007}
}
Comments
18 pages, LaTex, published in "Revista Mexicana de Fisica", V.44, N3, pp. 235-244, 1998