On the completeness of photon-added coherent states
J. M. Sixdeniers, K. A. Penson · Journal of Physics A Mathematical and General · 2001
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 (â † ) M | z ⟩, M = 0,1,2,...,, where â † 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.