Thomas-Fermi Theory

Part of the Texts and Monographs in Physics book series (TMP)


In this chapter we wish to study those problems from Thomas-Fermi theory whose solutions depend almost exclusively on the methods of the calculus of variations. Questions of validity and physical interpretation are discussed by Thirring [10.1] and Lieb and Simon [10.2] and in references quoted therein. Justification for statements which we do not prove below can be found in [10.1, 3].


Minimisation Problem Particle Number Fermi Theory Frechet Derivative Weakly Convergent Sequence 
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  1. 10.1
    Thirring, W.: A course in mathematical physics, vol. 4. Springer, Berlin Heidelberg 1986CrossRefGoogle Scholar
  2. 10.2
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  7. 10.5
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  8. 10.6
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  13. 10.10
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  14. 10.11
    Benguria, R., Brezis, H., Lieb, E.: The Thomas-Fermi-von Weizsäcker theory of atoms and molecules. Commun. Math. Phys.79(1981) 167–180CrossRefzbMATHADSMathSciNetGoogle Scholar
  15. 10.12
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  16. 10.13
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  18. 10.15
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  19. 10.16
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  20. 10.17
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  22. 10.18
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Further Reading

  1. Thirring, W.: A lower bound with the best possible constant for Coulomb Hamiltonians. Commun. Math. Phys.79(1981) 1–7CrossRefADSMathSciNetGoogle Scholar
  2. Dyson, F. J.: In: Brandeis University Summer Institute in Theoretical Physics 1966, vol. 1.Google Scholar
  3. M. Chretien, E. P. Gross and S. Deser (eds.). Gordon and Breach, New York 1978Google Scholar
  4. Lenard, A.: In: Statistical mechanics and mathematical problems. Lecture Notes in Physics20. Springer, Berlin Heidelberg 1973CrossRefGoogle Scholar
  5. Hille, E.: On the Thomas-Fermi equation. Proc. Nat. Acad. Sci. (USA)62(1969) 7–10CrossRefzbMATHADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Theoretische Physik, Fakultät für PhysikUniversität BielefeldBielefeldGermany
  2. 2.Department of MathematicsUniversity of Cape TownRondeboschSouth Africa

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