arXiv 1801.052322018-01-16quant-ph

受限氢原子的各种复杂性测度

Various complexity measures in confined hydrogen atom

Sangita Majumdar, Neetik Mukherjee, Amlan K. Roy

备注：: 15 pages, 4 tables, 4 figures
发表信息：: Chem. Phys. Lett. 687 322-329 (2017)
DOI：: 10.1016/j.cplett.2017.09.036

摘要：

在位置（$r$）和动量（$p$）空间中计算了受限氢原子的几种类似于\emph{LMC}和\emph{Fisher-Shannon}复杂性的统计测度.此外，这些量与雷尼熵（$R$）的更一般化的形式在这里探索。标度参数在指数部分的作用也被追求。在$r$和$p$空间中，将$α, β$作为$(\frac{2}{3},3)$来计算$R$。详细的系统性结果，这些措施相对于变化的限制半径$r_c$的低洼状态，如$1s$ - $3d,~4f$和$5g$。对于\emph{nodal}状态，例如$2s,~3s$和$3p$，随着$r_c$的进展，在$r$空间中出现最大值，随后是最小值，具有缩放参数的某些值。然而，相应的$p$ -空间结果缺乏这种独特的模式.这项研究揭示了许多其他有趣的特征。

英文摘要：

Several well-known statistical measures similar to \emph{LMC} and \emph{Fisher-Shannon} complexity have been computed for confined hydrogen atom in both position ($r$) and momentum ($p$) spaces. Further, a more generalized form of these quantities with Rényi entropy ($R$) is explored here. The role of scaling parameter in the exponential part is also pursued. $R$ is evaluated taking order of entropic moments $α, β$ as $(\frac{2}{3},3)$ in $r$ and $p$ spaces. Detailed systematic results of these measures with respect to variation of confinement radius $r_c$ is presented for low-lying states such as, $1s$-$3d,~4f$ and $5g$. For \emph{nodal} states, such as $2s,~3s$ and $3p$, as $r_c$ progresses there appears a maximum followed by a minimum in $r$ space, having certain values of the scaling parameter. However, the corresponding $p$-space results lack such distinct patterns. This study reveals many other interesting features.

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英文摘要：

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