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On the Quantum Theory of the Problem of the Two Bodies

Published online by Cambridge University Press:  24 October 2008

Extract

The problem of the two bodies has been treated on the new mechanics by Dirac, Pauli, and Schrödinger, who have independently derived the Balmer terms. The present paper is an attempt at a more complete solution. In particular, formulae are derived for the line intensities of the hydrogen spectrum, for the photoelectric effect and its inverse, and for the continuous absorption spectrum in the ultraviolet and in the X-ray regions. Also the probabilities of transition, deflection and capture are computed for the collision of an electron and an ion. Numerical values are only obtained, however, for the simplest line intensities. It is hoped to treat the problem in greater detail.

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Copyright
Copyright © Cambridge Philosophical Society 1926

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References

* Dirac, , Proc. Roy. Soc. A, 110, 501 (1926).CrossRefGoogle Scholar

Pauli, , Zeit. f. Phys. 36, 336 (1926).CrossRefGoogle Scholar

Schrödinger, , Ann. d. Phys. 79, 361 (1926).CrossRefGoogle Scholar

§ Kramers, , Intensities of Spectral Lines, Copenhagen, 1919.Google Scholar

Born, u. Jordan, Zeit. f. Phys. 34, 858 (1925).CrossRefGoogle Scholar

Schrödinger, , Ann. d. Phys. 79, 734 (1926).CrossRefGoogle Scholar

* The intensities of the hydrogen lines have been investigated by Pauli in a paper not yet published.Google Scholar

* I am indebted to Mr J. T. Edsahl for checking these calculations.Google Scholar

Fowler, , Phil. Mag. 50, 1079 (1925).CrossRefGoogle Scholar

Tolman, and Badger, , Phys. Rev. 27, 383 (1926).CrossRefGoogle Scholar

§ Kramers, , Phil. Mag. 46, 836 (1923).CrossRefGoogle Scholar

See, for an account of the mathematical methods, Schlesinger, , Differential-gleichungen, Vieweg, 1922Google Scholar, and Whittaker, and Watson, , Modern Analysis, Cambridge, Chap. XIV.Google Scholar

* I am much indebted to Dr P. A. M. Dirac for suggesting this procedure.Google Scholar

* This is impossible if one neglects transitions.Google Scholar

In this connection see a paper by Born, , Zeit. f. Phys. 37, 863 (1926).CrossRefGoogle Scholar

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