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The Dispersion Electrons in the One-Electron Problem
Published online by Cambridge University Press: 24 October 2008
Extract
In this paper we use Dirac's relativity quantum mechanics to derive the well-known Kramers-Heisenberg dispersion formula for an atom with one electron. The treatment is not limited to the case of a central field, but is quite general. An expression is also obtained for the dipole moment to which is due the incoherent scattering. The formulae obtained are similar to those obtained by O. Klein for the case of a central field. We find in this way an explicit expression for f, the number of dispersion electrons for any line of the optical spectrum (being a measure of the intensity of the line), in terms of the solutions of the four wave equations of Dirac's theory. It is further shown that the sum of the number of dispersion electrons for any state of the atom is not exactly unity, but differs from it by an amount of the order of 10−4. The result Σf = 1 has been shown by London to hold exactly for the simple wave equation as originally given by Schrödinger. It is here shown that the exact relativity treatment has a very small effect.
- Type
- Articles
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 3 , July 1929 , pp. 323 - 330
- Copyright
- Copyright © Cambridge Philosophical Society 1929
References
* Proc. Roy. Soc. A, CXVII, 610 (1928), CXVIII, 351 (1928).Google Scholar
† Zeit. für Phys., XLI, 407 (1927).Google Scholar
‡ See Darwin, , Proc. Roy. Soc. A, CXVIII, 654 (1928).CrossRefGoogle Scholar
§ Zeit. für Phys., XXXIX, 322 (1926).Google Scholar
* Darwin, , loc. cit.Google Scholar
† Klein, , loc. cit.Google Scholar
* See London, loc. cit., esp. p. 323.
† As, e.g., ibid., equation (3).
* See, e.g., Courant u. Hilbert, , Mathematische Physik, I, p. 36.Google Scholar