Perelomov and Barut-Girardello Su(1,1) coherent states for harmonic oscillator in one-dimensional half space

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 Delta x Delta p for these two coherent states are bound from below root 9/4 - 6/pi 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.