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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 291, Pages 43–63
(Mi znsl1621)
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This article is cited in 8 scientific papers (total in 8 papers)
Barut–Girardello Coherent states for the Gegenbauer oscillator
V. V. Borzova, E. V. Damaskinskyb a St. Petersburg State University of Telecommunications
b Military Technical University
Abstract:
For the Gegenbauer oscillator, which definition is suggested in this paper, for which the Gegenbauer (ultraspherical) polynomials plays the same role as the Hermite polynomials in the case of usual boson oscillator, we define the family of Barut–Girardello coherent states (the eigenstates of the relevant anihilation operator). We show the validity of unity resolution for this states and evaluate their overlaping. We also show that the given results reproduce the analogous results, obtained early, for the cases of Legendre and Chebyshev polynomials. In the later case we also construct the measure which participate in the unity resolution.
Received: 25.10.2002
Citation:
V. V. Borzov, E. V. Damaskinsky, “Barut–Girardello Coherent states for the Gegenbauer oscillator”, Questions of quantum field theory and statistical physics. Part 17, Zap. Nauchn. Sem. POMI, 291, POMI, St. Petersburg, 2002, 43–63; J. Math. Sci. (N. Y.), 125:2 (2005), 123–135
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https://www.mathnet.ru/eng/znsl1621 https://www.mathnet.ru/eng/znsl/v291/p43
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Abstract page: | 194 | Full-text PDF : | 61 |
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