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Note on the Interpretation of the Density Matrix in the Many-Electron Problem

  • P. A. M. Dirac (a1)

When we treat an atom containing a number n of electrons by the method of the self-consistent field, we assume that each electron has its own particular “orbit,” specified by a wave function (q|r) in four variables q. These four variables are usually taken to be the three coordinates of the electron together with a variable describing the spin, but according to the transformation theory of quantum mechanics, they may be any four independent commuting functions of the coordinates, momenta and spin variables.

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* Fock, Z. f. Physik, vol. 61, p. 126 (1930).

(r|q) is the conjugate complex function to (q|r).

* Proc. Camb. Phil. Soc. vol. xxvi, p. 376 (1930), equations (9), (10), (11).

When the q's take on continuous ranges of values, this is to be understood in terms of differentials in the usual way.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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