MEIXNER OSCILLATORS

Meixner oscillators have a ground state and an 'energy' spectrum that is equally spaced; they are a two-parameter family oi models that sati sfy a Hamiltonian equation with a difference operator. Meixner oscilla tors include as Limits and particular cases the Charlier, Kravchuk and Hermite (common quantum-mechanical) harmonic oscillators. By the Somm erfeld-Watson transformation they are also related with a relativistic model of the linear harmonic oscillator, built in terms of the Meixne r-Pollaczek polynomials, and their continuous weight function. We cons truct explicitly the corresponding coherent states with the dynamical symmetry group Sp(2,R). The reproducing kernel for the wavefunctions o f these models is also found.