Charlier Polynomials and Charlier Oscillator as Discrete Realization of the Harmonic Oscillator

The Charlier polynomials are used for constructing oscillator-like systems. We introduce coherent states of the system are defined and study the main properties (in particular, the (over)completeness property). We show that the coherent states on the associated uncertainty relation take the minimum value. In the case under consideration, the Mandel parameter vanishes, which corresponds to the Poisson statistics of quasiexcitation spectrum for the considered oscillator. Bibliography: 30 titles.__________Translated from Problemy Matematicheskogo Analiza, No. 30, 2005, pp. 3–15.