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Acta Physica Sinica

GLAUBER COHERENT STATE q-DEFORMED QUANTUM OSCILLATOR

Hao San-Ru, 长沙水利电力师范学院物理系,长沙410077

Published Jan 1, 1993• 4 citations
Publisher

Abstract

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.

DOI
10.7498/aps.42.1057

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Acta Physica Sinica•Jan 1, 1993•1 citation
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.
The energy level structure of the q deformed harmonic oscillator in a finite dimensional Hilbert space is studied.The Coherent states of the q deformed harmonic oscillator in a finite dimensional Hilbert space are constructed.It is shown that the energy level structure and the dynamic action are very different from that of usual harmonic oscillator due to the finiteness of the dimension of Hilbert space and the deformation parameter′s influence,and the coherent states are different from the Glauber coherent states.
Adopting the framework of the generalized q -deformed Heisenberg–Weyl algebra , we present a mathematical procedure which leads us to obtain analytical expressions for a general class of q -deformed coherent states associated with the different patterns of the energy spectrum exhibited by the nonlinear f -oscillator. In particular, we establish the properties of a small group of q -deformed coherent states for α > γ > 0 with emphasis on the resolution of unity. As an application of these properties, we investigate the Robertson–Schrödinger uncertainty relation and the squeezing effect for the deformed coordinate and momentum operators, which are defined in terms of the abstract elements of this algebra. Furthermore, we also obtain the Wigner function and the correct quantum-mechanical marginal distributions in phase space.