Acta Physica Academiae Scientiarum Hungaricae

, Volume 7, Issue 3, pp 357–364 | Cite as

On a new exchange potential

  • P. Szépfalusy


In the investigation of systems consisting of particles of spin 1/2 by the Hartree-Fock method there occurs the operator of exchange interaction. The semi-classical analogue of this operator is known for various interaction potentials. The purpose of this paper is to present a method which makes possible a more accurate determination of the semi-classical analogue of the exchange operator. The detailed calculations have been carried out for the Coulomb potential.


Wave Function Exchange Interaction Coulomb Potential Exchange Operator Exchange Potential 
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О новом обменном потенциале


При рассмтрении систем, состоящих из частиц с половинными спинами, методом Гартри—Фока появляется оператор обменного взаимодействия. Полуклассический аналог этого оператора известен в случае различных потенциалов взаимодействия. Целью работы является показать метод, дающий возможность более точно определить полуклассический аналог обменного оператора. Детальный расчет проведен в случае кулоновского потенциала.


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  1. 1.
    D. R. Hartree, Proc. Camb. Phil. Soc.,24, 89, 1928.CrossRefGoogle Scholar
  2. 2.
    V. Fock, Zs. f. Phys.,61, 126, 1930.CrossRefADSGoogle Scholar
  3. 3.
    P. A. M. Dirac, Proc. Camb. Phil. Soc.,26, 376, 1930.Dirac did not take into account the fact that the exchange interaction only occurs between particles of parallel spin and thus he obtained twice the correct result.zbMATHCrossRefGoogle Scholar
  4. 4.
    SeeP. Gombás, Die statistische Theorie des Atoms und ihre Anwendungen, p. 5, Springer, Wien, 1949.zbMATHGoogle Scholar
  5. 5.
    SeeP. Gombás, l. c. pp. 23–24.zbMATHGoogle Scholar
  6. 6.
    V. Fock, Zs. f. Phys.,81, 195, 1953. In this paperFock studied the exchange operator acting on a valency electron outside an atomic core of closed shells. However, this exchange operator completely agrees in form with the operator (10), provided the density of the atomic core is substituted by the total density of particles. ThusFock’s method can readily be applied to the operator (10).CrossRefADSGoogle Scholar
  7. 7.
    SeeP. Gombás, l. c. p. 6.zbMATHGoogle Scholar

Copyright information

© with the authors 1957

Authors and Affiliations

  • P. Szépfalusy
    • 1
  1. 1.Physical InstituteUniversity for Technical SciencesBudapest

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