Goudsmit and Uhlenbeck

This simplified treatment does not account for the fine-structure of the hydrogen spectrum. It has been shown by Dirac (22) that the assumption that the system conform to the principles of the quantum mechanics and of the theory of relativity leads to results which are to a first approximation equivalent to attributing to each electron a spin that is, a mechanical moment and a magnetic moment, and to assuming that the spin vector can take either one of two possible orientations in space. The existence of this spin of the electron had been previously deduced by Uhlenbeck and Goudsmit (23) from the empirical study of line spectra. This result is of particular importance for the problems of chemistry. 

Following the hypothesis of electron spin by Uhlenbeck and Goudsmit, P. A. M. Dirac (1928) developed a quantum mechanics based on the theory of relativity rather than on Newtonian mechanics and applied it to the electron. He found that the spin angular momentum and the spin magnetic moment of the electron are obtained automatically from the solution of his relativistic wave equation without any further postulates. Thus, spin angular momentum is an intrinsic property of an electron (and of other elementary particles as well) just as are the charge and rest mass. 

The postulates of quantum mechanics discussed in Section 3.7 are incomplete. In order to explain certain experimental observations, Uhlenbeck and Goudsmit introduced the concept of spin angular momentum for the electron. This concept is not contained in our previous set of postulates an additional postulate is needed. Further, there is no reason why the property of spin should be confined to the electron. As it turns out, other particles possess an intrinsic angular momentum as well. Accordingly, we now add a sixth postulate to the previous list of quantum principles. 

The spin (angular momentum) quantum number ms. In their interpretation of many features of atomic spectra Uhlenbeck and Goudsmit (1925) proposed for the electron a new property called spin angular momentum (or simply spin) and assumed that only two states of spin were possible. In relativistic (four-dimensional) quantum mechanics this quantum number is related to the symmetry properties of the wave function and may have one of the two values designated as A. 

Electron Spin. One of die properties of electrons that became evident during die study of optical spectra of atoms was that of electron spin. The suggestion was made by Uhlenbeck and Goudsmit in 1925 that one of die features of such spectra could be understood if each electron had associated with it a quantity called spin, which is similar in many ways to angular momentum. Each electron also has a certain magnetic moment which affects the energy in the presence of a magnetic field.2 This property also has been incorporated into the wave concepts of quantum mechanics. 

The value e/mc for the electron gyromagnetie ratio was first postulated by Uhlenbeck and Goudsmit and later shown to be a consequence of the Dirac electron theory. 

As already pointed out, terms such as wave function, electron orbit, resonance, etc., with which we describe the formulations and results of wave mechanics, are borrowed from classical mechanics of matter in which concepts occur which, in certain respects at least, show a correspondence to the wave mechanical concepts in question. The same is the case with the electron spin. In Bohr s quantum theory, Uhlenbeck and Goudsmit s hypothesis meant the introduction of a fourth quantum number j, which can only take on the values +1/2 and —1/2- In wave mechanics it means that the total wave function, besides the orbital function, contains another factor, the spin function. This spin function can be represented by a or (3, whereby, for example, a describes the state j = +1/2 and P that with s = —1/2. The correspondence with the mechanical analogy, the top, from which the name spin has been borrowed, is appropriate in so far that the laevo and dextro rotatory character, or the pointing of the top in the + or — direction, can be connected with it. A magnetic moment and a... 

This assumption was made by Uhlenbeck and Goudsmit, the discoverers of electron spin, and later shown [98] to be the correct value for an electron viewed as a rapidly rotating body, not anywhere exceeding c in tangential velocity. 

Following the hypothesis of electron spin by Uhlenbeck and Goudsmit, P. A. 

To explain this/me structure of atomic spectra, Uhlenbeck and Goudsmit proposed... 

The notion of electronic spin was first proposed by Uhlenbeck and Goudsmit in 1925 to account for the sphtting of some of the lines seen in atomic spectra. They and others showed that the electronic spin also accounted for the anomalous effects of magnetic fields (Zeeman effects) on the spectra of many atoms. However, it was necessary to postulate that the magnetic moment associated with electronic spin is not simply the product of the angular momentum and ejlmc, as is true of orbital magnetic moments, but rather twice this value. The extra factor of 2 is called the Lande g factor. When Dirac [33] reformulated quantum mechanics to be consistent... 

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