Estimates on derivatives of Coulombic wave functions and their electron densities
Estimates on derivatives of Coulombic wave functions and their electron densities
复制标题
库仑波函数导数及其电子密度的估计
DOI：
10.1515/crelle-2020-0047
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
T. O. Sorensen
中科院分区：
文献类型：
--
作者：
S. Fournais;T. O. Sorensen
摘要我们证明了非相对论库仑本征函数的所有导数的先验界，其中包括到多体势奇点的距离的负幂。我们用这些公式推导出相应的单电子密度ρ的所有导数的界，其中涉及到离核距离的负幂。从氢的基态可以看出，结果是自然的和最佳的。
Abstract We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions ψ, involving negative powers of the distance to the singularities of the many-body potential. We use these to derive bounds for all derivatives of the corresponding one-electron densities ρ, involving negative powers of the distance from the nuclei. The results are both natural and optimal, as seen from the ground state of Hydrogen.