The quantum theory of the electron

1928/02/01 by P. A. M. Dirac, Paul Adrien Maurice Dirac · 2 voices · 2,169 citations
Physics and Astronomy · #Experimental and Theoretical Physics Studies #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics

paper · doi:10.1098/rspa.1928.0023

published in Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 117(778), 610-624 (The Royal Society)

crossref issued 1928/02/01 · crossref published 1928/02/01 · crossref published-print 1928/02/01 · openalex publication_date 1928/02/01 · crossref created 2006/12/15 · openalex created_date 2016/06/24 · crossref deposited 2026/01/03 · openalex updated_date 2026/08/02 · crossref indexed 2026/08/07

Abstract

Abstract The new quantum mechanics, when applied to the problem of the structure of the atom with point-charge electrons, does not give results in agreement with experiment. The discrepancies consist of “duplexity ” phenomena, the observed number of stationary states for an electron in an atom being twice the number given by the theory. To meet the difficulty, Goudsmit and Uhlenbeck have introduced the idea of an electron with a spin angular momentum of half a quantum and a magnetic moment of one Bohr magneton. This model for the electron has been fitted into the new mechanics by Pauli,* and Darwin,† working with an equivalent theory, has shown that it gives results in agreement with experiment for hydrogen-like spectra to the first order of accuracy. The question remains as to why Nature should have chosen this particular model for the electron instead of being satisfied with the point-charge. One would like to find some incompleteness in the previous methods of applying quantum mechanics to the point-charge electron such that, when removed, the whole of the duplexity phenomena follow without arbitrary assumptions. In the present paper it is shown that this is the case, the incompleteness of the previous theories lying in their disagreement with relativity, or, alternatetively, with the general transformation theory of quantum mechanics. It appears that the simplest Hamiltonian for a point-charge electron satisfying the requirements of both relativity and the general transformation theory leads to an explanation of all duplexity phenomena without further assumption. All the same there is a great deal of truth in the spinning electron model, at least as a first approximation. The most important failure of the model seems to be that the magnitude of the resultant orbital angular momentum of an electron moving in an orbit in a central field of force is not a constant, as the model leads one to expect.

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Discussions

• ⚛️g-factor. El factor g de los leptones fue calculado por Dirac en 1928, deduciendo el Hamiltoniano de interacción entre el electrón y el fotón (doi.org/10.1098/rspa...). Como todos los leptones sigu [bsky, 1 points, 1 comments]
• I was reading Dirac's original paper from 1928, and I noticed this equation Is it just me, or it's supposed to be $$\rho_{mn} = -\frac{e}{2mc^2}\lbrace ih (\psi_m \frac{\partial \bar{\psi_n}}{\partial [stackexchange, 1 points]

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