Generalized coherent states for oscillators connected with Meixner and Meixner—Pollaczek polynomials

Abstract

The authors continue to study generalized coherent states for oscillator-like systems connected with a given family of orthogonal polynomials. In this work, we consider oscillators connected with Meixner and Meixner— Pollaczek polynomials and define generalized coherent states for these oscillators. A completeness condition for these states is proved by solution of a related classical moment problem. The results are compared with the other authors ones. In particular, we show that the Hamiltonian of the relativistic model of a linear harmonic oscillator can be treated as the linearization of a quadratic Hamiltonian, which arises naturally in our formalism. Bibliography: 56 titles.