Positivity and lower bounds to the decay of the atomic one-electron density

2006/08/08 by Søren Fournais, Maria Hoffmann-Ostenhof, Fournais, Søren +6
Materials Science · Mathematics · Physics and Astronomy · #35B04 #35B40 (secondary) #35J10 #81Q05 (primary) #81V45 #Advanced Chemical Physics Studies #FOS: Physical sciences #Magnetism in coordination complexes #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:35B04 #msc:35B40 #msc:35J10 #msc:81Q05 #msc:81V45

paper · pdf · doi:10.48550/arxiv.math-ph/0608022

20 pages

arxiv created 2006/08/08 · openalex publication_date 2006/08/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate properties of the spherically averaged atomic one-electron density rho~(r). For a rho~ which stems from a physical ground state we prove that rho~ > 0. We also give exponentially decreasing lower bounds to rho~ in the case when the eigenvalue is below the corresponding essential spectrum.

Related

• Revisiting the Z-dependence of the electron density at the nuclei
• Upper Estimates for Electronic Density in Heavy Atoms and Molecules
• On the Locality of Physics in Metals, Semiconductors, and Insulators
• One-Particle Properties of an Inhomogeneous Interacting Electron Gas
• Eigenvalue estimates for the Coulombic one-particle density matrix and the kinetic energy density matrix