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Many-Electron Approaches in Physics, Chemistry and Mathematics pp 207–217Cite as

The Quantum Energy Agrees with the Müller Energy up to Third Order

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Part of the book series: Mathematical Physics Studies ((MPST))

Abstract

We show that the ground state energy \(E_\mathrm {M}(Z)\) of the Müller functional of (neutral) atoms of atomic number \(Z\) equals to the quantum mechanical ground state energy \(E_\mathrm {S}(Z)\) up order \(o(Z^{5/3})\), i.e., \( E_\mathrm {M}(Z)= E_\mathrm {S}(Z)+ o(Z^{5/3}). \)

©Heinz Siedentop. Based on a translation of J. Phys. A: Math. Theor. 42, 085201 (2009), doi:10.1088/1751-8113/42/8/085201.

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Notes

  1. 1.

    Here and in the following \(\mathrm {C}\) denote a generic constant.

  2. 2.

    Note the operator \(P\) introduced this way is no projection.

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Acknowledgments

Partial support by the SFB-TR 12 of the DFG is gratefully acknowledged.

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Authors and Affiliations

  1. Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstraße 39, 80333, Munich, Germany

    Heinz Siedentop

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  1. Heinz Siedentop
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Correspondence to Heinz Siedentop .

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Editors and Affiliations

  1. Institut für Analysis Und Algebra Carl-Friedrich-Gauss-Fakultät, Technische Universität Braunschweig, Braunschweig, Germany

    Volker Bach

  2. Institute for Mathematics, Freie Universität Berlin, Berlin, Germany

    Luigi Delle Site

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Siedentop, H. (2014). The Quantum Energy Agrees with the Müller Energy up to Third Order. In: Bach, V., Delle Site, L. (eds) Many-Electron Approaches in Physics, Chemistry and Mathematics. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-06379-9_11

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