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TMF, 1990, Volume 85, Number 1, Pages 64–73 (Mi tmf5931)  

This article is cited in 15 scientific papers (total in 15 papers)

Difference analogs of the harmonic oscillator

N. M. Atakishiyev, S. K. Suslov


Abstract: Two different models of a difference oscillator are discussed on the basis of the factorization method.

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English version:
Theoretical and Mathematical Physics, 1990, 85:1, 1055–1062

Bibliographic databases:

Received: 12.01.1990

Citation: N. M. Atakishiyev, S. K. Suslov, “Difference analogs of the harmonic oscillator”, TMF, 85:1 (1990), 64–73; Theoret. and Math. Phys., 85:1 (1990), 1055–1062

Citation in format AMSBIB
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\by N.~M.~Atakishiyev, S.~K.~Suslov
\paper Difference analogs of~the harmonic oscillator
\jour TMF
\yr 1990
\vol 85
\issue 1
\pages 64--73
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1083952}
\zmath{https://zbmath.org/?q=an:1189.81099}
\transl
\jour Theoret. and Math. Phys.
\yr 1990
\vol 85
\issue 1
\pages 1055--1062
\crossref{https://doi.org/10.1007/BF01017247}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990FK88200007}


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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. N. M. Atakishiyev, S. K. Suslov, “A realization fo the $q$-harmonic oscillator”, Theoret. and Math. Phys., 87:1 (1991), 442–444  mathnet  crossref  mathscinet  zmath  isi
    2. A. S. Zhedanov, ““Hidden symmetry” of Askey–Wilson polynomials”, Theoret. and Math. Phys., 89:2 (1991), 1146–1157  mathnet  crossref  mathscinet  zmath  isi
    3. A. S. Zhedanov, “Weyl shift of $q$-oscillator and $q$-polynomials”, Theoret. and Math. Phys., 94:2 (1993), 219–224  mathnet  crossref  mathscinet  zmath  isi
    4. N. M. Atakishiyev, S. K. Suslov, “The Clebsch–Gordan coefficients for the quantum algebra $SU_{q}(2)$”, Theoret. and Math. Phys., 98:1 (1994), 1–7  mathnet  crossref  mathscinet  zmath  isi
    5. Sh. M. Nagiyev, “Difference Schrödinger equation and $q$-oscillator model”, Theoret. and Math. Phys., 102:2 (1995), 180–187  mathnet  crossref  mathscinet  zmath  isi
    6. S. P. Novikov, I. A. Dynnikov, “Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds”, Russian Math. Surveys, 52:5 (1997), 1057–1116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. S. P. Novikov, “Difference Schrödinger Operators”, Proc. Steklov Inst. Math., 224 (1999), 250–265  mathnet  mathscinet  zmath
    8. S. V. Smirnov, “Cyclic $q$-chains”, St. Petersburg Math. J., 15:5 (2004), 795–811  mathnet  crossref  mathscinet  zmath
    9. V. V. Borzov, E. V. Damaskinsky, “Coherent states for generalized oscillator in finite-dimensional Hilbert space”, J. Math. Sci. (N. Y.), 143:1 (2007), 2738–2753  mathnet  crossref  mathscinet  zmath
    10. V. V. Borzov, “Generalized oscillator and its coherent states”, Theoret. and Math. Phys., 153:3 (2007), 1656–1670  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Kurt Bernardo Wolf, Luis Edgar Vicent, “The Fourier $\mathsf U(2)$ Group and Separation of Discrete Variables”, SIGMA, 7 (2011), 053, 18 pp.  mathnet  crossref  mathscinet
    12. Odake S., Sasaki R., “Discrete quantum mechanics”, J. Phys. A: Math. Theor., 44:35 (2011), 353001  crossref  isi
    13. Elchin I. Jafarov, Neli I. Stoilova, Joris Van der Jeugt, “Deformed $\mathfrak{su}(1,1)$ algebra as a model for quantum oscillators”, SIGMA, 8 (2012), 025, 15 pp.  mathnet  crossref  mathscinet
    14. Borzov V.V., Damaskinsky E.V., “The Algebra of Two Dimensional Generalized Chebyshev-Koornwinder Oscillator”, J. Math. Phys., 55:10 (2014), 103505  crossref  isi
    15. Roy Oste, “Doubling (Dual) Hahn Polynomials: Classification and Applications”, SIGMA, 12 (2016), 003, 27 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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