Atomic Systems

  • Walter Thirring


The hydrogen atom is so simple that a complete mathematical analysis can be made. This analysis was a watershed of atomic physics.


Atomic System Trial Function Essential Spectrum Point Spectrum Schrodinger Equation 
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Chapter 4, General

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Chapter 4, Specific Section 4.1

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(4.3.45; 2)

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Section 4.4

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  1. See reference [3], section XII.6.Google Scholar
  2. B. Simon. Resonances in n-Body Quantum Systems with Dilation Analytic Potentials and the Foundations of Time-Dependent Perturbation Theory. Ann. Math. 97, 247–274, 1973.MATHCrossRefGoogle Scholar


  1. B. Simon. N Body Scattering in the Two-Cluster Region. Commun. Math. Phys. 58, 205–210, 1978.ADSCrossRefGoogle Scholar
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  1. See references for section 3.6.Google Scholar
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  1. P. Hertel, E. H. Lieb, and W. Thirring. Lower Bound to the Energy of Complex Atoms. J. Chem. Phys. 62, 3355–3356, 1975.ADSCrossRefGoogle Scholar

(4.5.27; 1)

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(4.5.27; 2)

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  1. See reference [6].Google Scholar


  1. See reference for (4.2.19).Google Scholar


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  3. J. M. Combes and R. Seiler. Regularity and Asymptotic Properties of the Discrete Spectrum of Electronic Hamiltonians. Int. J. Quanturn Chem. 14, 213–229, 1978.CrossRefGoogle Scholar


  1. See reference for (4.2.19).Google Scholar


  1. E. H. Lieb and B. Simon. Monotonicity of the Electronic Contribution to the Born-Oppenheimer Energy. J. Phys. B11, L537–L542, 1978.MathSciNetADSGoogle Scholar
  2. M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof, in prep. (for the proof using the differential inequality).Google Scholar


  1. See the second reference for (3.5.31).Google Scholar

(4.6.28; 2)

  1. A subsequent justification of the formal argument of C. A. Coulson; see R. Ahlrichs. Convergence Properties of the Intermolecular Force Series (1/R-Expansion). Theor. Chim. Acta 41, 7–15, 1976.CrossRefGoogle Scholar

(4.6.28; 5)

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(4.6.28; 7)

  1. See reference [19].Google Scholar

(4.6.31; I)

  1. R. F. Alvarez-Estrada and A. Galindo. Bound States in some Coulomb Systems. Il Nuovo Cim. 44B, 47–66, 1978.MathSciNetADSGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1981

Authors and Affiliations

  • Walter Thirring
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of ViennaAustria

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