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On the Atomic Energy Asymptotics

  • C. L. Fefferman
  • L. A. Seco
Conference paper

Abstract

Consider an atom consisting of N quantized electrons at positions x i and a nucleus fixed at the origin. The Schrödinger Hamiltonian of such a system is given by
$${H_{Z,N}} = \sum\limits_{i = 1}^N {\left( { - {\Delta _{{x_i}}} - \frac{Z} {{\left| {{x_i}} \right|}}} \right)} + \frac{1} {2}\sum\limits_{i \ne j} {\frac{1} {{\left| {{x_i} - {x_i}} \right|}}} $$
acting on \( = \wedge _{i = 1}^N{L^2} \) (R3) (in this exposition, in order to simplify notation, we neglect spin.) Define the ground state of an atom of charge Z by
$$ E\left( Z \right) = {\kern 1pt} \mathop {\inf }\limits_N \mathop {\inf }\limits_{\mathop {\left\| \Psi \right\| = 1}\limits_{\Psi \in } } \;\left\langle {{H_{Z,N\Psi ,\Psi }}} \right\rangle $$
.

Keywords

Finite Order Energy Asymptotics Smooth Potential Antisymmetric Product Semiclassical Asymptotics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • C. L. Fefferman
    • 1
  • L. A. Seco
    • 2
  1. 1.Princeton UniversityUSA
  2. 2.California Institute of TechnologyUSA

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