Geodesic
Generalized coherent states for oscillators connected with Meixner and Meixner--Pollachek polynomials
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 18, Tome 317 (2004), pp. 66-93

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We are continuing here the study of generalized coherent states for the oscillator-like systems connected with the given set of orthogonal polynomials. In this work we concider the case of Meixner and Meixner–Pollachek polynomials. We construct the oscillator-like systems associated with these polynomials and define their coherent states. By the solution of the related classical moment problem we prove the overcompleteness of constructed families of coherent states. We compare the obtained results with the results of other works. In particular, we shaw that the Hamiltonian of the relativistic model of linear harmonic oscillator can be concidered as special linearization of the quadratic Hamiltonin naturally appearing in our approach. 
@article{ZNSL_2004_317_a4,
     author = {V. V. Borzov and E. V. Damaskinsky},
     title = {Generalized coherent states for oscillators connected with {Meixner} and {Meixner--Pollachek} polynomials},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {66--93},
     publisher = {mathdoc},
     volume = {317},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_317_a4/}
}
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V. V. Borzov; E. V. Damaskinsky. Generalized coherent states for oscillators connected with Meixner and Meixner--Pollachek polynomials. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 18, Tome 317 (2004), pp. 66-93. http://geodesic.mathdoc.fr/item/ZNSL_2004_317_a4/