@article{SIGMA_2012_8_a92,
author = {Yusuf Sucu and Nuri Unal},
title = {Coherent {States} for {Tremblay{\textendash}Turbiner{\textendash}Winternitz} {Potential}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2012},
volume = {8},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a92/}
}
Yusuf Sucu; Nuri Unal. Coherent States for Tremblay–Turbiner–Winternitz Potential. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a92/
[1] Calogero F., “Solution of a three-body problem in one dimension”, J. Math. Phys., 10 (1969), 2191–2197 | DOI | MR
[2] Evans N. W., “Group theory of the Smorodinsky–Winternitz system”, J. Math. Phys., 32 (1991), 3369–3375 | DOI | MR | Zbl
[3] Friš J., Mandrosov V., Smorodinsky Ya.A., Uhlíř M., Winternitz P., “On higher symmetries in quantum mechanics”, Phys. Lett., 16 (1965), 354–356 | DOI | MR
[4] Glauber R. J., “Photon correlations”, Phys. Rev. Lett., 10 (1963), 84–86 | DOI | MR
[5] Glauber R. J., “The quantum theory of optical coherence”, Phys. Rev., 130 (1963), 2529–2539 | DOI | MR
[6] Gradshteyn I. S., Ryzhik I. M., Table of integrals, series, and products, Academic Press, New York, 1980 | Zbl
[7] Kalnins E. G., Kress J. M., Miller W., “Superintegrability and higher order integrals for quantum systems”, J. Phys. A: Math. Theor., 43 (2010), 265205, 21 pp., arXiv: arXiv:1002.2665 | DOI | MR | Zbl
[8] Kalnins E. G., Miller W., Pogosyan G. S., “Superintegrability and higher order constants for classical and quantum systems”, Phys. Atomic Nuclei, 74 (2011), 914–918, arXiv: arXiv:0912.2278 | DOI | MR
[9] Olshanetsky M. A., Perelomov A. M., “Quantum integrable systems related to Lie algebras”, Phys. Rep., 94 (1983), 313–404 | DOI | MR
[10] Quesne C., “Superintegrability of the Tremblay–Turbiner–Winternitz quantum Hamiltonians on a plane for odd $k$”, J. Phys. A: Math. Theor., 43 (2010), 082001, 10 pp., arXiv: arXiv:0911.4404 | DOI | MR | Zbl
[11] Schrödinger E., “Der stetige Übergang von der Mikro- zur Makromechanik”, Naturwissenschaften, 14 (1926), 664–666 | DOI
[12] Tremblay F., Turbiner A. V., Winternitz P., “An infinite family of solvable and integrable quantum systems on a plane”, J. Phys. A: Math. Theor., 42 (2009), 242001, 10 pp., arXiv: arXiv:0904.0738 | DOI | MR | Zbl
[13] Tempesta P., Turbiner A. V., Winternitz P., “Exact solvability of superintegrable systems”, J. Math. Phys., 42 (2001), 4248–4257, arXiv: hep-th/0011209 | DOI | MR | Zbl
[14] Tremblay F., Turbiner A. V., Winternitz P., “Periodic orbits for an infinite family of classical superintegrable systems”, J. Phys. A: Math. Theor., 43 (2010), 015202, 14 pp., arXiv: arXiv:0910.0299 | DOI | MR | Zbl
[15] Turbiner A., “Hidden algebra of three-body integrable systems”, Modern Phys. Lett. A, 13 (1998), 1473–1483, arXiv: solv-int/9805003 | DOI | MR
[16] Unal N., “Coherent states for Smorodinsky–Winternitz potentials”, Cent. Eur. J. Phys., 7 (2009), 774–785 | DOI
[17] Unal N., “Parametric time-coherent states for the hydrogen atom”, Phys. Rev. A, 63 (2001), 052105, 8 pp. | DOI
[18] Unal N., “Parametric-time coherent states for Morse potential”, Can. J. Phys., 80 (2002), 875–881 | DOI
[19] Unal N., “Parametric-time coherent states for Smorodinsky–Winternitz potentials”, J. Math. Phys., 48 (2007), 122107, 20 pp. | DOI | MR
[20] Unal N., “Parametric-time coherent states for the generalized MIC-Kepler system”, J. Math. Phys., 47 (2006), 122105, 15 pp. | DOI | MR
[21] Unal N., “Path integration and coherent states for the 5{D} hydrogen atom”, Fluctuating Paths and Fields, eds. W. Janke, A. Pelster, H. J. Schmidt, M. Bachmann, World Sci. Publ., River Edge, NJ, 2001, 73–81 | DOI | MR
[22] Unal N., “Quasi-coherent states for harmonic oscillator with time-dependent parameters”, J. Math. Phys., 53 (2012), 012102, 8 pp. | DOI | MR
[23] Unal N., “Smorodinsky–Winternitz potentials: coherent, state approach”, Phys. Atomic Nuclei, 74 (2011), 1758–1769 | DOI
[24] Watson G. N., A treatise on the theory of Bessel functions, Cambridge University Press, London, 1922 | MR
[25] Wolfes J., “On the three-body linear problem with three-body interaction”, J. Math. Phys., 15 (1974), 1420–1424 | DOI | MR