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Acta Scientiarum Naturalium Universitatis Neimongol

Quantum Properties of q-deformed Harmonic Oscillator and Their Coherent States in Electric Field

Bai Xian

Published Jan 1, 2001• 0 citations
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Abstract

The energy level structure and eigen wave functions of the q deformed harmonic oscillator in electric field are obtained by using the q differential.Glauber coherent states are constructed and its quantum properties are studied.It is shown that the dynamic actions are different from that of usual harmonic oscillator due to the deformation parameter′s influence.When q=1,q deformed harmonic oscillator degrades to usual harmonic oscillator.

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Chinese Journal of Quantum Electronics•Jan 1, 2001•0 citations
The energy level structure and eigen wave functions of the q deformed harmonic oscillator in electric field are obtained by using the q differential.Glauber coherent states are constructed and its quantum properties are studied.It is shown that the dynamic actions are different from that of usual harmonic oscillator due to the deformation parameter′s influence.When q=1,q deformed harmonic oscillator degrades to usual harmonic oscillator.
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.
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.
In this research, we study the coherent states of a deformed nonlinear harmonic oscillator. We use the perturbation theory to compute eigenstates and eigen-values ​​for a deformed nonlinear harmonic oscillator and then define the generalized coherent states based on the Gazeau-Klauder formulation. Then, using the Mandel parameter and the second-order correlation function, we will investigate the statistical properties of the system. The analysis shows that the coherent states for a deformed and non-deformed nonlinear harmonic oscillator follows the sub-Poissonian and super-Poissonian statistics, and exhibits the antibunching and bunching effects, respectively. In addition, we show that the anti-correlation function for a deformed nonlinear oscillator is strongly fluctuating and irregular. Also, the anti-correlation function of a non-deformed nonlinear harmonic oscillator shows the phenomena of collapse and revival of fractional revelations. We also examine the limits of different parameters so that the obtained results are valid.