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TMF, 2007, Volume 153, Number 3, Pages 363–380 (Mi tmf6142)  

This article is cited in 2 scientific papers (total in 2 papers)

Generalized oscillator and its coherent states

V. V. Borzov

St. Petersburg State University of Telecommunications

Abstract: We construct a system (a generalized oscillator) that is similar to the oscillator and is related to a system of orthogonal polynomials on the real axis. We define coherent states in the Fock space associated with the generalized oscillator. In the example of the generalized oscillator related to the Gegenbauer polynomials, we prove the (super)completeness of these coherent states, i.e., we construct a measure determining a partition of unity. We present a formula that allows calculating the Mandel parameter for the constructed coherent states.

Keywords: orthogonal polynomials, harmonic oscillator, generalized oscillator, creation operator, annihilation operator, coherent state, Mandel parameter

DOI: https://doi.org/10.4213/tmf6142

Full text: PDF file (476 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 153:3, 1656–1670

Bibliographic databases:

Received: 05.02.2007

Citation: V. V. Borzov, “Generalized oscillator and its coherent states”, TMF, 153:3 (2007), 363–380; Theoret. and Math. Phys., 153:3 (2007), 1656–1670

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf6142
  • https://doi.org/10.4213/tmf6142
  • http://mi.mathnet.ru/eng/tmf/v153/i3/p363

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Borzov, E. V. Damaskinsky, “Generalized coherent states for oscillators associated with the Charlier $q$-polynomials”, Theoret. and Math. Phys., 155:1 (2008), 536–543  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. V. V. Borzov, E. V. Damaskinsky, “$N$-symmetric Chebyshev polynomials in a composite model of a generalized oscillator”, Theoret. and Math. Phys., 169:2 (2011), 1561–1572  mathnet  crossref  crossref  mathscinet  adsnasa  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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