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2009 | 7 | 1 | 147-159
Tytuł artykułu

Gazeau-Klauder type coherent states for hypergeometric type operators

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Hypergeometric type operators are shape invariant, and a factorization into a product of first order differential operators can be explicitely described in the general case. Some additional shape invariant operators depending on several parameters are defined in a natural way by starting from this general factorization. The mathematical properties of the eigenfunctions and eigenvalues of the operators thus obtained depend on the values of the parameters involved. We study the parameter dependence of orthogonality, square integrability and monotony of the eigenvalue sequence. The results obtained allow us to define certain systems of Gazeau-Klauder type coherent states and to describe some of their properties. Our systematic study recovers a number of well-known results in a natural, unified way and also leads to new findings.
Wydawca

Czasopismo
Rocznik
Tom
7
Numer
1
Strony
147-159
Opis fizyczny
Daty
wydano
2009-03-01
online
2009-01-08
Twórcy
  • Faculty of Physics, University of Bucharest, PO Box 76 - 54, Post Office 76, Bucharest, Romania, ncotfas@yahoo.com
Bibliografia
  • [1] F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 267 (1995) http://dx.doi.org/10.1016/0370-1573(94)00080-M[Crossref]
  • [2] L. Infeld, T.E. Hull, Rev. Mod. Phys. 23, 21 (1951) http://dx.doi.org/10.1103/RevModPhys.23.21[Crossref]
  • [3] J.R. Klauder, B.S. Skagerstam, Coherent States - Applications in Physics and Mathematical Physics (World Scientific, Singapore,1985)
  • [4] A.M. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986)
  • [5] S.T. Ali, J.-P. Antoine, J.-P. Gazeau, Coherent States, Wavelets and Their Generalizations (Springer, New York, 2000)
  • [6] N. Cotfas, Cent. Eur. J. Phys. 2, 456 (2004) http://dx.doi.org/10.2478/BF02476425[Crossref]
  • [7] A.F. Nikiforov, S.K. Suslov, V.B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable (Springer, Berlin, 1991)
  • [8] N. Cotfas, Cent. Eur. J. Phys. 4, 318 (2006) http://dx.doi.org/10.2478/s11534-006-0023-0[Crossref]
  • [9] M.A. Jafarizadeh, H. Fakhri, Ann. Phys. NY 262, 260 (1998) http://dx.doi.org/10.1006/aphy.1997.5745[Crossref]
  • [10] J.P. Gazeau, J.R. Klauder, J. Phys. A: Math. Gen. 32, 133 (1999) http://dx.doi.org/10.1088/0305-4470/32/1/013[Crossref]
  • [11] Bateman Project, Erdelyi (Ed.), Integral transformations, vol. I (McGraw-Hill, New York, 1954) 349
  • [12] J.-P. Antoine, J.-P. Gazeau, P. Monceau, J.R. Klauder, K.A. Penson, J. Math. Phys. 42, 2349 (2001) http://dx.doi.org/10.1063/1.1367328[Crossref]
  • [13] A.O. Barut, L. Girardello L, Commun. Math. Phys. 21, 41 (1971) http://dx.doi.org/10.1007/BF01646483[Crossref]
  • [14] I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals and Series (Academic Press, 1980)
  • [15] B. Roy, P. Roy, Phys. Lett. A 296, 187 (2002) http://dx.doi.org/10.1016/S0375-9601(02)00143-3[Crossref]
  • [16] Y. L. Luke, The Special Functions and Their Approximations, vol. I (Academic Press, New York, 1969) 157
  • [17] A. Chenaghlou, O. Faizy, J. Math. Phys. 49, 022104 (2008)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-008-0138-6
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