The quantum theory of the electron
01 Feb 1928-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 117, Iss: 778, pp 610-624
TL;DR: In this article, it was shown that the incompleteness of the previous theories lying in their disagreement with relativity or, alternatetically, with the general transformation theory of quantum mechanics leads to an explanation of all duplexity phenomena.
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.
Citations
More filters
TL;DR: Weyl and Dirac semimetals as discussed by the authors are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry, and they have generated much recent interest.
Abstract: Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.
3,407 citations
Cites background from "The quantum theory of the electron"
...Acknowledgements 54 References 54 I. INTRODUCTION In 1928 P.A.M. Dirac proposed – in the first successful reconciliation of special relativity and quantum mechanics – his now eponymous Dirac equation (Dirac, 1928)....
[...]
TL;DR: In this paper, the authors discuss the effect of the Verschrgnkung on the performance of the experimentators in terms of the results of the experiments they conducted, and present an analysis of the verifiability of their results.
Abstract: § 71. Die Au]hebung der ,,Verschrdinkung". Das Ergebnis abhdingig vom Willen des Experimentators. W i r kehren wieder zum al lgemeinen Fal l der ,Ve r sch r~nkung" znrfick, ohne gerade den besonderen Fa i l eines ~{eBvorgangs im Ange zu haben, wie soeben. Die Erwar tungska ta loge zweier 1{6> per A und B sollen sich durch vorf ibergehende Wechse lwi rkung verschr~nkt haben. J e t z t sollen die K6rper wieder ge t renn t seth. ] )ann kann ich einen davon, e twa B, hernehmen und meine unter m a x i m a l gewordene Kenntn is yon ihm du tch ?¢Iessungen sukzessive zu einer max ima len erggnzen. Ich behaup te : sobald mi r das z u m erstenmal gelingt, und nicht eher, wird erstens die Verschrgnkung gerade gel6st sein und werde ich zweitens durch die Messungen an B u n t e r Ausnf i tzung der Kondi t ionalsa tze , die bestanden, max ima le Kermtnis such yon A erworben haben. D e n n erstens Meibt die Kem~tnis yore Gesarntsys tem framer maximal , well sie du t ch gu ie und genaue Messungen keinesfalls ve rdorben wird. Zwei tens: Kondi t ionalsgtze yon der F o r m ,,wenn an A . . . . . . dann an B . . . . . " , kann es n icht mehr geben, sobald wi t yon B einen Maximalka ta log erlangt haben. Denn der ist nieht bedingt und zu ibm kann f iberhaupt nichts auf B Bezfigliches mehr h inzut re ten . Dr i t t ens : Kond i t i ona l s i t z e in umgekehr t e r R ich tung (,,wenn an B . . . . . . dann an A . . . . . ") lassen sich in S~itze fiber A allein umwandeln , well j a alle Wahrsche in l ichke i ten ffir B schon bedingungslos bekann t sind. Die Ver sch r in kung ist a lso rest los beseit igt , und da die Kenntn is v o m Gesamtsys t em max ima l gebl ieben ist, kann sie nur dar in bestehen, dab zum Maximalka ta tog ffir B ein ebensolcher ffir A h inzut r i t t . Es kann abe t such nicht e twa vorkommen, dab A indirekt , durch die Messungen an B, schon max ima l bekann t wird, bevor B es noch ist. Denn dann funkt ionieren alle Schlfisse in umgekehr t e r Richtung, d. h. B ist es au th . Die Sys teme werden gleichzeit ig max ima l bekannt , wie behaupte t . Nebenbei bemerkt , wfirde das such geiten, wenn man das Messen nicht gerade auf eines der beiden Sys teme beschrltnkt. Abe t das In teressante ist gerade, dab m a n es auf eines der beiden beschrgnken lcann; dab mari dami t ans ZieI kommt . Welche 5{essungen an B und in welcher iReihenfolge sie vo rgenommen werden, fat ganz der ~Nill-
2,739 citations
TL;DR: The Basis Set Exchange (BSE) is described, a Web portal that provides advanced browsing and download capabilities, facilities for contributing basis set data, and an environment that incorporates tools to foster development and interaction of communities.
Abstract: Basis sets are some of the most important input data for computational models in the chemistry, materials, biology, and other science domains that utilize computational quantum mechanics methods. Providing a shared, Web-accessible environment where researchers can not only download basis sets in their required format but browse the data, contribute new basis sets, and ultimately curate and manage the data as a community will facilitate growth of this resource and encourage sharing both data and knowledge. We describe the Basis Set Exchange (BSE), a Web portal that provides advanced browsing and download capabilities, facilities for contributing basis set data, and an environment that incorporates tools to foster development and interaction of communities. The BSE leverages and enables continued development of the basis set library originally assembled at the Environmental Molecular Sciences Laboratory.
2,642 citations
[...]
TL;DR: In solid-state materials with strong relativistic spin-orbit coupling, charge currents generate transverse spin currents as discussed by the authors and the associated spin Hall and inverse spin Hall effects distinguish between charge and spin current where electron charge is a conserved quantity but its spin direction is not.
Abstract: In solid-state materials with strong relativistic spin-orbit coupling, charge currents generate transverse spin currents. The associated spin Hall and inverse spin Hall effects distinguish between charge and spin current where electron charge is a conserved quantity but its spin direction is not. This review provides a theoretical and experimental treatment of this subfield of spintronics, beginning with distinct microscopic mechanisms seen in ferromagnets and concluding with a discussion of optical-, transport-, and magnetization-dynamics-based experiments closely linked to the microscopic and phenomenological theories presented.
2,178 citations
TL;DR: In this paper, the authors compared Dirac's theory of the positron to those proposed by Born and showed that the field strength of large fields differs strongly from those of small fields.
Abstract: [arXiv:physics/0605038]: According to Dirac’s theory of the positron, an electromagnetic field tends to create pairs of particles which leads to a change of Maxwell’s equations in the vacuum. These changes are calculated in the special case that no real electrons or positrons are present and the field varies little over a Compton wavelength. The resulting effective Lagrangian of the field reads: $\cal{L} = \frac{\displaystyle 1}{\displaystyle 2} (\cal{E}^2 - \cal{B}^2) + \frac{\displaystyle e^2}{\displaystyle h c}\int_0^\infty e^{-\eta} \frac{\displaystyle d \eta}{\displaystyle\eta^3}\left\{ i \eta^2 (\cal{EB})\cdot \frac{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB})}\right) + conj.}{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB}})\right) - conj. } + \vert\cal{E}\vert^2 + \frac{\displaystyle\eta^2}{\displaystyle 3} (\cal{B}^2 - \cal{E}^2)\right\}$. $\cal{E}$, $\cal{B}$ field strengths. $\vert\cal{E}_k\vert = \frac{\displaystyle m^2 c^3}{\displaystyle e\hbar} = \frac{\displaystyle 1}{\displaystyle 137} \frac{\displaystyle e}{\displaystyle(e^2/m c^2)^2}$ critical field strengths. The expansion terms in small fields (compared to $\cal{E}$) describe light-light scattering. The simplest term is already known from perturbation theory. For large fields, the equations derived here differ strongly from Maxwell’s equations. Our equations will be compared to those proposed by Born. Original German abstract [Z.Phys. 98(1936)714]: Aus der Diracschen Theorie des Positrons folgt, da jedes elektromagnetische Feld zur Paarerzeugung neigt, eine Abanderung der Maxwellschen Gleichungen des Vakuums. Diese Abanderungen werden fur den speziellen Fall berechnet, in dem keine wirklichen Elektronen und Positronen vorhanden sind, und in dem sich das Feld auf Strecken der Compton-Wellenlange nur wenig andert. Es ergibt sich fur das Feld eine Lagrange-Funktion: $\cal{L} = \frac{\displaystyle 1}{\displaystyle 2} (\cal{E}^2 - \cal{B}^2) + \frac{\displaystyle e^2}{\displaystyle h c}\int_0^\infty e^{-\eta} \frac{\displaystyle d \eta}{\displaystyle\eta^3}\left\{ i \eta^2 (\cal{EB})\cdot \frac{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB}})\right) + konj}{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB})}\right) - konj } + \vert\cal{E}\vert^2 + \frac{\displaystyle\eta^2}{\displaystyle 3} (\cal{B}^2 - \cal{E}^2)\right\}$. ($\cal{E}$, $\cal{B}$ Kraft auf das Elektron. $\vert\cal{E}_k\vert = \frac{\displaystyle m^2 c^3}{\displaystyle e\hbar} = \frac{\displaystyle 1}{\displaystyle ,,137``} \frac{\displaystyle e}{\displaystyle (e^2/m c^2)^2}$ „Kritische Feldstarke“.) Ihre Entwicklungsglieder fur (gegen $\vert\cal{E}_k\vert$) kleine Felder beschreiben Prozesse der Streuung von Licht an Licht, deren einfachstes bereits aus einer Storungsrechnung bekannt ist. Fur grose Felder sind die hier abgeleiteten Feldgleichungen von den Maxwellschen sehr verschieden. Sie werden mit den von Born vorgeschlagenen verglichen.
2,059 citations