Meixner Polynomials and ID Para-Bose Oscillator

Вадим Васильевич Борзов, Eugeniy Viktorovich Damaskinsky

Rafael G. Campos

Manfred Schmutz

Ha Huy Bang

Вадим Васильевич Борзов, Eugeniy Viktorovich Damaskinsky

The investigation of the generalized coherent states for oscillator-like systems connected with given family of orthogonal polynomials is continued. In this work we consider oscillators connected with Meixner and Meixner-Pollaczek polynomials and define generalized coherent states for these oscillators. The completeness condition for these states is proved by the solution of the 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 linear harmonic oscillator can be thought of as the linearization of the quadratic Hamiltonian which naturally arised in our formalism.

Natig M. Atakishiyev, E. I. Jafarov, Sh. M. Nagiyev +1 more

We discuss a difference model of the linear harmonic oscillator based on the Meixner polynomials. As limit and special cases, it contains difference oscillator models in terms of the Kravchuk and Charlier polynomials, as well as the wavefunctions of the linear harmonic oscillator in quantum mechanics. We show that the dynamical group is SU(1,1) and construct explicitly the corresponding coherent state. The reproducing kernel for the wavefunctions of the Meixner model is also found.