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.

中文翻译：

---

库仑波函数的导数及其电子密度的估计

我们证明了非相对论库伦本征函数ψ的所有导数的先验界，涉及到多体势奇点的距离的负幂。我们使用这些来推导出相应单电子密度 ρ 的所有导数的界限，涉及到原子核距离的负幂。从氢的基态来看，结果既是自然的又是最佳的。