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Abstract

The Hamilton operator Ĥ of an atom with Z-electrons and Z-protons (in the nucleus) is given by (Schiff [51])
$$\hat{H} = - \frac{{{{\hbar }^{2}}}}{{2{{m}_{e}}}}\sum\limits_{{i = 1}}^{Z} {{{\Delta }_{i}} - \frac{{{{\hbar }^{2}}}}{{2{{m}_{N}}}}{{\Delta }_{N}} - \frac{{{{e}^{2}}}}{{4\pi {{ \in }_{0}}}}\sum\limits_{{i = 1}}^{Z} {\left( {\frac{Z}{{|{{r}_{i}} - {{r}_{N}}|}} - \sum\limits_{{j \ne i}}^{Z} {\frac{1}{{|{{r}_{i}} - {{r}_{j}}|}}} } \right)} }$$
where m e is the mass of the electron and m N the mass of the nucleus. The first term describes the kinetic contributions from the electrons and the second the kinetic contribution from the nucleus. The third term gives the interaction of the nucleus with the electrons (attractive force) and the fourth the interaction of the electrons (repulsive force)

Keywords

Wave Function Variational Principle Helium Atom Eigenvalue Equation Hamilton Operator 
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 Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Willi-Hans Steeb
    • 1
  1. 1.International School for Scientific ComputingRand Afrikaans UniversityJohannesburgSouth Africa

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