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Abstract

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].

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References

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Further Reading

  • Thirring, W.: A lower bound with the best possible constant for Coulomb Hamiltonians. Commun. Math. Phys.79(1981) 1–7

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  • Dyson, F. J.: In: Brandeis University Summer Institute in Theoretical Physics 1966, vol. 1.

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  • M. Chretien, E. P. Gross and S. Deser (eds.). Gordon and Breach, New York 1978

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  • Lenard, A.: In: Statistical mechanics and mathematical problems. Lecture Notes in Physics20. Springer, Berlin Heidelberg 1973

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  • Hille, E.: On the Thomas-Fermi equation. Proc. Nat. Acad. Sci. (USA)62(1969) 7–10

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© 1992 Springer-Verlag Berlin Heidelberg

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Blanchard, P., Brüning, E. (1992). Thomas-Fermi Theory. In: Variational Methods in Mathematical Physics. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82698-6_11

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  • DOI: https://doi.org/10.1007/978-3-642-82698-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

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