2007/09/30 by Zhixin Qian · 1 citation
Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Bound state #Charge (physics) #Electron #Electron density #Excited state #Ground state #Ion #Quantum Mechanics and Non-Hermitian Physics #Upper and lower bounds #physics.atom-ph #physics.chem-ph
paper · pdf · doi:10.1088/1751-8113/41/8/085305
published in Journal of Physics A Mathematical and Theoretical 41(8), 085305 (Institute of Physics) · 4 pages
arxiv created 2008/01/02 · openalex publication_date 2008/02/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A lower bound for , the second derivative of the spherically averaged atomic electronic density at the nucleus, and an upper bound for , the third derivative, are obtained, respectively. It is shown that, for the ground state, and , where Z is the charge of the nucleus, and ρ(0) is the electron density at the nucleus. Tighter bounds for and are also reported which are valid for both the ground state and excited states. Explicit illustration with the example of one-electron atomic ions is given.