标题： 所有离散多维氢化态的解析香农信息熵 显示英文标题

标题： Analytical Shannon information entropies for all discrete multidimensional hydrogenic states

摘要： 多维氢态的熵不确定性度量量化了系统电子概率密度空间离域性的多个方面。 香农熵是最合适的不确定性度量，用于量化电子的扩展性，并数学上形式化海森堡不确定性原理，部分原因在于它不依赖于其多维定义域中的任何特定点。 在本工作中，从第一性原理得到了多维氢系统所有离散定态的径向和角部分的香农熵；也就是说，它们以状态的主量子数和磁超量子数$(n,\mu_1,\mu_2,\ldots,\mu_{D-1})$、系统的维度$D$和核电荷$Z$的解析紧凑形式给出。 给出了准球形态的总香农熵的显式表达式，这些态是$D$维氢系统的一个相关类特定态，由超量子数$\mu_1=\mu_2\ldots=\mu_{D-1}=n-1$特征化，包括基态。 显示英文摘要

摘要： The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty measure to quantify the electronic spreading and to mathematically formalize the Heisenberg uncertainty principle, partially because it does not depend on any specific point of their multidimensional domain of definition. In this work the radial and angular parts of the Shannon entropies for all the discrete stationary states of the multidimensional hydrogenic systems are obtained from first principles; that is, they are given in terms of the states' principal and magnetic hyperquantum numbers $(n,\mu_1,\mu_2,\ldots,\mu_{D-1})$, the system's dimensionality $D$ and the nuclear charge $Z$ in an analytical, compact form. Explicit expressions for the total Shannon entropies are given for the quasi-spherical states, which conform a relevant class of specific states of the $D$-dimensional hydrogenic system characterized by the hyperquantum numbers $\mu_1=\mu_2\ldots=\mu_{D-1}=n-1$, including the ground state.