On the basis of the q-binomial theorem we construct the q-binomial state for a q-deformed boson which interpolates between the q-number state and the q-coherent state. The properties of the q-binomial state are also discussed.
Using the q analog of the Holstein-Primakoff boson realization of the su(2) generators, we show that a type of q-deformed binomial state that corresponds to the Heine distribution can be identified as an su(2)q coherent state. This fact is a q extension of the fact that the ordinary binomial state is a particular su(2) coherent state when the Holstein-Primakoff transformation is employed.
By making use of the Fock States of the q-deformed quantum oscillator which possesses the symmetry of quantum group, we construct the Glauber coherent state of the q-deformed quantum oscillator (the q-Glauber coherent state ㄧα>q). We discuss the of completeness properties, particle number distribution, oscillator strength distribution and the minimal uncertainty principle of the q-Glauber coherent states, and point out that the coherent degree of the q-Glauber coherent state can be described by the parameter q.