The Vector Model and the Pauli Principle

M. H. Johnson, Jr.
Phys. Rev. 43, 627 – Published 15 April 1933
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Abstract

The vector model is examined in the light of the quantum theory of wave fields. First the distributions of electrons among the electronic states are limited to correspond to the atomic states arising from one electronic configuration. A set of independent angular momentum vectors 11, 12,...S1, S2... is found, in which one orbital and one spin vector are associated with each group of electronic states, rather than individual electrons, having given values of the quantum numbers n and l. Any other vector T may be decomposed into a sum of independent vectors ti, one associated with each of the same group of electronic states. The usual commutation relations obtain among the vectors ti, li and si. On further limiting the distributions to correspond to atomic states arising from electronic configurations containing no equivalent electrons, it is shown that the matrix of Σkf(lk0, sk0) (an operator in coordinate space in which f is any algebraic function of the components of 1 and s) can be constructed from the vectors 11, 12...S1, S2,... according to the usual laws of matrix mechanics.

  • Received 21 February 1933

DOI:https://doi.org/10.1103/PhysRev.43.627

©1933 American Physical Society

Authors & Affiliations

M. H. Johnson, Jr.*

  • New York University

  • *National Research Fellow.

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Issue

Vol. 43, Iss. 8 — April 1933

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