Pointwise estimates on derivatives of Coulombic wave functions and their electron densities

Abstract

We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions, 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, involving negative powers of the distance from the nuclei. The results are both natural and optimal, as seen from the ground state of Hydrogen.

arXiv comment46 pp

References in corpus (3)

• Sharp regularity results for many-electron wave functions
• A new proof of the analyticity of the electronic density of molecules
• Ellipticity of quantum mechanical Hamiltonians in the edge algebra

Cited by in corpus (3)

• Analyticity of the one-particle density matrix
• Weighted analyticity of Hartree-Fock eigenfunctions
• ${\mathrm{RCD}}^{\ast }(K,N)$ spaces and the geometry of multi-particle Schrödinger semigroups