Resolution of the Identity of the Classical Hardy Space by Means of Barut-Girardello Coherent States

Dušan Popov, Nicolina Pop, Viorel Chiritoiu +2 more

Hossein Fakhri, Alireza Chenaghlou

Quanhui Liu, H. ZHUO

The Perelomov and the Barut–Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below [Formula: see text] that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut–Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.

Arno Böhm, Hai Viet Bui

S. Twareque Ali, Stephan De Bièvre

Alireza Chenaghlou, Omid Faizy

The Barut-Girardello and Klauder-Perelomov coherent states for the Kravchuk functions are constructed. It is shown that the resolution of unity condition is satisfied for both of the coherent states. Also in the N+1-dimensional Hilbert space spanned by the Kravchuk eigenstates, the appropriate measure and analytic function are obtained.