Abstract
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.
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References
F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 267 (1995)
L. Infeld, T.E. Hull, Rev. Mod. Phys. 23, 21 (1951)
J.R. Klauder, B.S. Skagerstam, Coherent States — Applications in Physics and Mathematical Physics (World Scientific, Singapore,1985)
A.M. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986)
S.T. Ali, J.-P. Antoine, J.-P. Gazeau, Coherent States, Wavelets and Their Generalizations (Springer, New York, 2000)
N. Cotfas, Cent. Eur. J. Phys. 2, 456 (2004)
A.F. Nikiforov, S.K. Suslov, V.B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable (Springer, Berlin, 1991)
N. Cotfas, Cent. Eur. J. Phys. 4, 318 (2006)
M.A. Jafarizadeh, H. Fakhri, Ann. Phys. NY 262, 260 (1998)
J.P. Gazeau, J.R. Klauder, J. Phys. A: Math. Gen. 32, 133 (1999)
Bateman Project, Erdelyi (Ed.), Integral transformations, vol. I (McGraw-Hill, New York, 1954) 349
J.-P. Antoine, J.-P. Gazeau, P. Monceau, J.R. Klauder, K.A. Penson, J. Math. Phys. 42, 2349 (2001)
A.O. Barut, L. Girardello L, Commun. Math. Phys. 21, 41 (1971)
I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals and Series (Academic Press, 1980)
B. Roy, P. Roy, Phys. Lett. A 296, 187 (2002)
Y. L. Luke, The Special Functions and Their Approximations, vol. I (Academic Press, New York, 1969) 157
A. Chenaghlou, O. Faizy, J. Math. Phys. 49, 022104 (2008)
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Cotfas, N. Gazeau-Klauder type coherent states for hypergeometric type operators. centr.eur.j.phys. 7, 147–159 (2009). https://doi.org/10.2478/s11534-008-0138-6
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DOI: https://doi.org/10.2478/s11534-008-0138-6