UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2024-11-23 18:19

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Conference: Bucharest University Faculty of Physics 2009 Meeting


Section: Theoretical Physics and Applied Mathematics Seminar


Title:
Gazeau-Klauder Coherent States for Hypergeometric Type Operators


Authors:
Nicolae Cotfas


Affiliation:
University of Bucharest, Faculty of Physics


E-mail
ncotfas@yahoo.com


Keywords:
orthogonal polynomials, associated special functions, hypergeometric type operators, Gazeau-Klauder coherent states.


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.