Borzov, V. V.; Damaskinsky, E. V. Generalized coherent states for oscillators associated with the Charlier \(q\) -polynomials. (English. Russian original) Zbl 1155.81339 Theor. Math. Phys. 155, No. 1, 536-543 (2008); translation from Teor. Mat. Fiz. 155, No. 1, 39-46 (2008). Summary: We continue studying the generalized coherent states for oscillator-like systems associated with a given family of orthogonal polynomials. We consider the case of generalized oscillators generated by the Charlier \(q\)-polynomials. Cited in 3 Documents MSC: 81R30 Coherent states 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics Keywords:deformed oscillator; coherent state; orthogonal polynomials; Charlier \(q\)-polynomial PDFBibTeX XMLCite \textit{V. V. Borzov} and \textit{E. V. Damaskinsky}, Theor. Math. Phys. 155, No. 1, 536--543 (2008; Zbl 1155.81339); translation from Teor. Mat. Fiz. 155, No. 1, 39--46 (2008) Full Text: DOI References: [1] A. Perelomov, Generalized Coherent States and Their Applications, Springer, Berlin (1986). · Zbl 0605.22013 [2] J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics, Benjamin, New York (1968). [3] V. V. Dodonov, J. Opt. B, 4, No. 1, R1–R33 (2002). [4] R. Floreanini and L. Vinet, Lett. Math. Phys., 22, 45–54 (1991). · Zbl 0745.33008 [5] E. V. Damaskinsky and P. P. Kulish, Zap. Nauchn. Sem. LOMI, 199, 81–90 (1992). [6] N. M. Atakishiyev, E. I. Jafarov, Sh. M. Nagiyev, and K. B. Wolf, Rev. Mexicana Fis., 44, 235–244 (1998); arXiv:math-ph/9807035v1 (1998). [7] A. Odzijewicz, M. Horowski, and A. Tereszkiewicz, J. Phys. A, 34, 4353–4376 (2001). · Zbl 0978.81084 [8] V. V. Borzov and E. V. Damaskinsky, Zap. Nauchn. Sem. POMI, 335, 75–99 (2006). [9] V. V. Borzov, Theor. Math. Phys., 153, 1656–1670 (2007). · Zbl 1146.81029 [10] R. Koekoek and R. F. Swarttouw, ”The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue,” Report No. 94-05, Delft Univ. of Technology, Delft (1994); arXiv:math/9602214v1 [math.CA] (1996). [11] V. V. Borzov, Integral Transform. Spec. Funct., 12, 115–138 (2001); arXiv:math/0002226v1 [math.CA] (2000). · Zbl 1026.33007 [12] V. V. Borzov, E. V. Damaskinsky, and P. P. Kulish, Rev. Math. Phys., 12, 691–710 (2000). [13] V. V. Borzov and E. V. Damaskinsky, Integral Transform. Spec. Funct., 13, 547–554 (2002); arXiv:math/0101215v1 [math.QA] (2001). · Zbl 1023.33005 [14] R. Askey and S. K. Suslov, J. Physics A, 26, L693–L698 (1993); arXiv:math/9307206v1 [math.CA] (1993). · Zbl 0859.33021 [15] R. Askey and S. K. Suslov, Lett. Math. Phys., 29, 123–132 (1993); arXiv:math/9307207v1 [math.CA] (1993). · Zbl 0919.33010 [16] J. R. Klauder, K. A. Penson, and J.-M. Sixdeniers, Phys. Rev. A, 64, 013817 (2001). [17] V. V. Borzov and E. V. Damaskinsky, ”Coherent states and uncertainty relations for generalized oscillators connected with the given families of orthogonal polynomials,” in: Proc. Intl. Semin. Day on DIFFRACTION 2005 (I. V. Andronov, ed.), St. Petersburg State Univ., St. Petersburg (2005), pp. 40–49. [18] V. V. Borzov and E. V. Damaskinsky, Zap. Nauchn. Sem. POMI, 308, 48–66 (2004). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.