Part of the Lecture Notes in Physics book series (LNP, volume 300)


Wigner Function Bohr Atom Scott Correction Paragraph Read Nonrelativistic Mechanic 
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  1. 1.
    The outstanding textbook on TF theory is still P. Gombás, Die statistische Theorie des Atoms and ihre Anwendungen (Springer, Wien, 1949). Then there is the review article N.H.March, Adv.Phys.6,1 (1957). A more recent introductory text is N.H.March, Self-consistent Fields in Atoms (Pergamon, Oxford, 1975).Google Scholar
  2. 2.
    L.H.Thomas, Proc.Cambridge Phil.Soc. 23, 542 (1926); E.Fermi, Rend. Lincei 6, 602 (1927); D.R.Hartree, Proc.Cambridge Phil.Soc. 24, 89 (1928); V.Fock, Zschr.f.Phys. 61, 126 (1930).Google Scholar
  3. 3.
    In the form of a textbook this material has been presented by W. Thirring, Lehrbuch der Mathematischen Physik, Vo1.4: Quantenmechanik großer Systeme (Springer, Wien-New York, 1980). A recent re-view is E.H.Lieb, Rev.Mod.Phys.53, 603 (1981). A treatment with emphasis on thermal properties is given by J.Messer, Temperature Dependent Thomas-Fermi Theory (Lecture Notes in Physics, Vol.147) (Springer, Berlin-Heidelberg-New York, 1981).Google Scholar
  4. 4.
    Models of screened Bohr atoms have been studied to some extent by R.Shakeshaft and L.Spruch, Phys.Rev. A 23, 2118 (1981). Their emphasis is on the oscillatory terms, about which we shall have to say something in Chapter Five.Google Scholar
  5. 5.
    This statement is frequently called the Hellmann-Feynman theorem. Both Hellmann (1933) and Feynman (1939), however, only rediscovered what had been known before. It is, indeed, difficult to imagine how quantum mechanics could have been developed without such a central tool. The theorem appears explicitly in Pauli's review of 1933, in Van Vleck's book of 1932, and in a paper by Güttinger in 1931. The latter contains, to my knowledge, the explicit statement for the first time. The various references are: P.Güttinger, Zschr.f.Phys. 73, 169(1931); J.H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Oxford University Press, 1932)Google Scholar
  6. 4.
    J. Schwinger, cited in Footnote 2 of Chapter Three.Google Scholar
  7. 5.
    I.K. Dmitrieva and G.I. Plindov, cited in Footnote 10 of Chapter Three.Google Scholar
  8. 6.
    From Ref.11 of Chapter Three.Google Scholar
  9. 7.
    J.M.S. Scott, cited in Footnote 1 of Chapter Three.Google Scholar
  10. 8.
    The number appearing here is 2.248 = 4~ 16-19~ 1a+4>1a 12+12~ ~,~ n=1 nn=1 n n=1 m=1 n mn=1 m=1 n m 4 = 4 x 1.036928-19 x 90 + 4 x 1.265738 +12 x 1.13347Google Scholar
  11. 9.
    W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965)Google Scholar
  12. 10.
    D.A. Kirzhnits and G.V. Shpatakovskaya, Zh. Eksp. Teor. Fiz. 62, 2082 (1972) (Sov. Phys.-JETP 35, 1088 (1972)] used methods related of those of Chapter Five to study shell effects in atomic densities. Their results are encouraging, but hardly satisfactory.Google Scholar
  13. 11.
    E.P. Wigner, cited in Footnote 5 of Chapter Four. We do not include the factors of 2n into the definition of the Wigner function.-A recent review of this subject is M. Hillary, R.F. O'Connell, M.O. Scully, and E.P. Wigner, Phys. Rep. 106, 121 (1984).Google Scholar

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