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Meixner Oscillators

Natig M. Atakishiyev·Elchin I. Jafarov·Shakir M. Nagiev·Kurt B. Wolf
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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,$\Re$). The reproducing kernel for the wavefunctions of these models is also found.

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Natig M. Atakishiyev, Elchin I. Jafarov, Shakir M. Nagiev, Kurt B. Wolf. 1998-07-31. Meixner Oscillators. https://arxiv.org/abs/math-ph/9807035

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