Annales Henri Poincaré

, Volume 13, Issue 8, pp 1733–1744 | Cite as

A New Estimate on the Two-Dimensional Indirect Coulomb Energy

  • Rafael D. Benguria
  • Pablo Gallegos
  • Matěj Tušek


We prove a new lower bound on the indirect Coulomb energy in two-dimensional quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the Lieb–Solovej–Yngvason bound with a smaller constant, \({C = (4/3)^{3/2} \sqrt{5 \pi -1} \approx 5.90 < C_{\rm LSY} = 192 \sqrt{2 \pi} \approx 481.27}\), which also involves an additive gradient energy term of the single particle density.


Coulomb Repulsion Gradient Term Electronic Repulsion Single Particle Density Littlewood Maximal Function 
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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Rafael D. Benguria
    • 1
  • Pablo Gallegos
    • 1
  • Matěj Tušek
    • 1
  1. 1.Departmento de FísicaP. Universidad Católica de ChileSantiagoChile

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