Gazeau-Klauder type coherent states for hypergeometric type operators

• Authors: Nicolae Cotfas
• Languages of publication: EN

Abstracts

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.

Keywords

EN

orthogonal polynomials; associated special functions; hypergeometric type operators; Gazeau-Klauder coherent states

Discipline

• 02.30.Gp: Special functions
• 03.65.-w: Quantum mechanics[see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics]

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2009
• Volume: 7
• Issue: 1
• Pages: 147-159

Dates

published

1 - 3 - 2009

online

8 - 1 - 2009

Contributors

author

Nicolae Cotfas

• Faculty of Physics, University of Bucharest, PO Box 76 - 54, Post Office 76, Bucharest, Romania

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Identifiers

DOI

10.2478/s11534-008-0138-6