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

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

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English version:
Theoretical and Mathematical Physics, 2007, 153:3, 1656–1670

Bibliographic databases:

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
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
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