Meixner Oscillators

Details Meixner Oscillators Meixner Oscillators

1998-07-31

arxiv.org/abs/math-ph/9807035v1

Rev.Mex.Fis. 44 (1998) 235-244

Physics

Mathematical Physics

18 pages, LaTex, published in "Revista Mexicana de Fisica", V.44, N3, pp. 235-244, 1998

Scientific paper

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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