On the completeness of photon-added coherent states

Citation
Jm. Sixdeniers et Ka. Penson, On the completeness of photon-added coherent states, J PHYS A, 34(13), 2001, pp. 2859-2866
Citations number
15
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
34
Issue
13
Year of publication
2001
Pages
2859 - 2866
Database
ISI
SICI code
0305-4470(20010406)34:13<2859:OTCOPC>2.0.ZU;2-K
Abstract
We demonstrate explicitly the completeness of photon-added coherent states (PACSs), introduced by Agarwal and Tara (Agarwal G S and Tara K 1991 Phys. Rev. A 43 492) and defined, up to normalization, by ((a) over cap (dagger)) (M) \z], M = 0, 1, 2,..., where (a) over cap (dagger) is the boson creation operator and \z] are conventional Glauber-Klauder coherent states. We find the analytical form of the positive weight function in their resolution of unity by solving the associated Stieltjes power-moment problem. We furnish an example of generation of another set of PACSs which are complete.