Third derivative of the one-electron density at the nucleus
Mathematical Physics
2015-06-26 v1 math.MP
Abstract
We study electron densities of eigenfunctions of atomic Schroedinger operators. We prove the existence of rho~'''(0), the third derivative of the spherically averaged atomic density rho~ at the nucleus. For eigenfunctions with corresponding eigenvalue below the essential spectrum we obtain the bound rho~'''(0) \leq -(7/12)Z^3 rho~(0), where Z denotes the nuclear charge. This bound is optimal.
Cite
@article{arxiv.math-ph/0607004,
title = {Third derivative of the one-electron density at the nucleus},
author = {Søren Fournais and Maria Hoffmann-Ostenhof and Thomas Østergaard Sørensen},
journal= {arXiv preprint arXiv:math-ph/0607004},
year = {2015}
}
Comments
28 pages