有限维希尔伯特空间中的q－相干态和q－变形谐振子动力学

The q-Coherent States and Dynamics of the q-Deformed Harmonic Oscillator in a Finite-Dimensional Hilbert Space

本文研究了有限维希尔伯特空间中ｑ－变形谐振子的ｑ－相干态，结果表明，ｑ－相干态有一些非平庸的特性，而其他的相干态可作为ｑ－相干态的特殊情形考虑，ｑ－谐振子的动力学特性最初在ｑ－相干态得以讨论，对于一些简单的情形分析了正交算符ｑ－相干态的ｑ－压缩的时间演化。

The q-coherent states(q-CSs) of the q-deformed harmonic oscillator(q-HO) in a finite-dimensional Hilbert space(FDHS)are introduced. It is shown that the q-CSs have some nontrivial properties and some other CSs may be considered as special cases of the q-CSs. The dynamical behaviours of the q-HO initially prepared in the q-CSs are studied. The time evolution of the q-squeezing of the q-CSs for the quadrature operators are analyzed for some simple cases.