中心势下量子态Rényi复杂度比的性质
Properties of Rényi complexity ratio of quantum states for central potential
摘要：
对三维和多维量子系统引入了两个密度函数的Rényi复杂度比。定义了几种密度函数的局部化性质，利用Lebesgue测度证明了Rényi复杂度比的近连续性的五个定理.证明和研究了不同量子系统的Rényi复杂度比的一些性质。给出了伪调和势和一类等谱势解的Rényi熵、Rényi复杂度比和基于Rényi熵的整数阶统计复杂度的精确解析形式.对一些双原子分子（CO，NO，N $_2$，CH，H $_2$，和ScH）和一些其它量子系统，证明了Rényi复杂度比的一些性质.
英文摘要：
Rényi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of Rényi complexity ratio are proved by Lebesgue measure. Some properties of Rényi complexity ratio are demonstrated and investigated for different quantum systems. Exact analytical forms of Rényi entropy, Rényi complexity ratio, statistical complexities based on Rényi entropy for integral order have been presented for solutions of pseudoharmonic and a family of isospectral potentials. Some properties of Rényi complexity ratio are verified for some diatomic molecules (CO, NO, N$_2$, CH, H$_2$, and ScH) and for some other quantum systems.
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