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A Theory of Hartree's Atomic Fields

Published online by Cambridge University Press:  24 October 2008

J. A. Gaunt
J. A. Gaunt
Affiliation:
Trinity College
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Extract

In a recent communication to this Society Dr Hartree has put forward a method for calculating the field of anatom containing many electrons. Each orbit—to borrow a metaphor from the old quantum theory—is related to a wave-function Ψ which obeys Schrödinger's equation. The potential energy used in this equation is due partly to the field of the nucleus, and partly to the fields of the electrons in the other orbits. The latter are calculated upon Schrödinger's interpretation of the wave-function, that |Ψ|2 is the density of charge, measured in electronic charges per unit volume. It is not the purpose of this paper to discuss the practical methods of obtaining wave-functions which reproduce the fields from which they are derived; but to relate these wave-functions and their energy parameters to those of the accepted theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 24 , Issue 2 , April 1928 , pp. 328 - 342
Copyright
Copyright © Cambridge Philosophical Society 1928

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References

* Hartree, D. R., Proc. Camb. Phil. Soc. XXIV, pp. 89–132 (1928).CrossRefGoogle Scholar

* This argument is borne out by calculations with the symmetrical wave-functions of the hydrogen atom. Denoting each state by its principal quantum number, and using Hartree's units, we have

* Dr Hartree kindly calculated this for me.