## Über nicht kombinierende Terme in der neueren Quantentheorie [Parts I-II, complete]. [Offered with:] Zur Erklärung einiger Eigenschaften der Spektren aus der Quantenmechanik des Drehelektrons [Parts I – III, complete].

Berlin: Julius Springer, 1926-28.

First editions, very rare offprint issues, of the papers that laid the foundations of the role of symmetry in quantum mechanics. “Wigner was a member of the race of giants that reformulated the laws of nature after the quantum mechanics revolution of 1924-25. In a series of papers on atomic and molecular structure, written between 1926 and 1928, Wigner laid the foundations for both the application of group theory to quantum mechanics and for the role of symmetry in quantum mechanics” (David J. Gross, ‘Symmetry in Physics: Wigner’s legacy,’ *Physics Today*, December 1995, pp. 46-50). Wigner was awarded the Nobel Prize in Physics in 1963 “for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles.”

*Provenance*: the last three offprints with the signature of German physicist Gregor Wentzel (1898-1978), who made important contributions to quantum mechanics; he is best known for the Wentzel-Kramers-Brillouin (WKB) approximation for finding approximate solutions to linear partial differential equations with spatially varying coefficients.

“Eugene Paul Wigner (1902-1995) contributed in a seminal way to theoretical physics. He is distinguished from other physicists who laid the foundations of quantum mechanics from the mid-1920s by his pioneering application of group theory and symmetry principles to quantum mechanics… Steven Weinberg has seen in the introduction of symmetry principles to physics the core of the revolutionary world view which has come to dominate modern physics: ‘Out of the fusion of relativity with quantum mechanics has evolved a new view of the world, one in which matter has lost its central role. This role has been usurped by the principles of symmetry, some of them hidden from view in the present state of the universe…’

“Wigner was a key figure in building the new language Weinberg is writing about, especially in the domains of quantum mechanics and fundamental particle theory. While Wigner was not alone in carrying out this momentous project, he was a pioneer in applying symmetry considerations and group theory on a grand scale to quantum mechanics… while Hermann Weyl is sometimes thought of as the originator of the group-theoretic approach in quantum mechanics, Wigner’s groundbreaking papers on group theory appeared before Weyl’s important work on the subject” (M. Chayut, ‘From the Periphery: the genesis if Eugene P. Wigner’s application of group theory to quantum mechanics,’ *Foundations of Chemistry* 3 (2001), 55-78).

“In the spring of 1926, Heisenberg had written a paper [‘Mehrkörperproblem und Resonanz in der Quantenmechanik,’ *Zeitschrift für Physik*, 38 Band, pp. 411-426] on quantum states of two identical electrically charged oscillators symmetrically coupled to each other. These, he found, separate into two sets of states, one symmetric, the other antisymmetric, under exchange of the oscillator coordinates. He further discovered that radiative transitions can occur only between states within each set, never between one set and the other. He went on to conjecture that non-combining sets should likewise exist if the number of identical particles is larger than two, but had not yet found a proof. Six weeks later, this work led Heisenberg to give the theory of a famous, yet unsolved two-electron problem, the spectrum of the helium atom.

“Wigner, who had read these papers soon after his return to Berlin, had become interested in this more-than-n identical particle problem. He rapidly mastered the case n = 3 (without spin) [the first offered paper]. His methods were rather laborious; for example, he had to solve a (reducible) equation of degree six. It would be pretty awful to go on in this way to higher n. So he went to consult the mathematician Johnny von Neumann. In the late 1950s Wigner explained to me what happened next…

“When he posed his question to von Neumann – Wigner told me – Johnny walked to a corner of the room, faced the wall, and started mumbling to himself. After a while he turned around and said: ‘You need the theory of group characters.’ At that moment Eugene had no idea what that theory was about. Whereupon von Neumann went to Issai Schur, obtained reprints of two of his papers, and gave them to Wigner. ‘[Those were] so easy to read, and of course it was clear that that was the solution.’ Within weeks, he had completed a second paper, now for the general n-particle problem [the second offered paper]. It contains these lines: ‘It is clear that one can hardly apply these elementary methods [he had used for n = 3] to the case of 4 electrons, since the computational difficulties get to be too large. There exists, however, a well-developed mathematical theory which one can use here: . . . group theory. . . . Herr von Neumann has kindly directed me to the relevant literature. . . . When I told Herr von Neumann the result of the calculations for n = 3, he correctly predicted the general result’ … Thus did group theory enter quantum mechanics.

“Wigner has said later: ‘I had a bad conscience because I felt that I should have published [that] second paper together with von Neumann.’ Joint publications did soon follow, however, three papers on atomic spectra which take account of the spin of the electron” (Pais, *The Genius of Science*, p. 335).

“Wigner perfected the group-theoretical ‘explanation of certain properties of spectra’ in three later communications [the last three offered papers] by taking care of the specific ‘quantum mechanics of the spinning electron,’ which he signed together with his friend John von Neumann and submitted in December 1927, February 1928 and June 1928, respectively… Von Neumann frequently came from Berlin to discuss matters with Wigner, who recalled: ‘These papers were written principally by me, but I felt that I had to express my gratitude to von Neumann for having introduced me to the work of Frobenius and Schur; therefore I proposed to him that we should publish them together.’

“The authors began their first paper with the remark that ‘the purpose of the present note is to use Pauli’s description of the rotating electron for an explanation of certain spectroscopic rules – by a method which has already been applied by one of the authors to derive a part of the spectroscopic experiences from quantum mechanics (without the rotating electron!) [Part I, p. 203], and announced the following programme: (1) to obtain the kinematics of the electron from Pauli’s idea; (2) to apply the theory to derive those spectroscopic laws that are strictly valid if the magnetic interactions of the spinning electron are included; (3) to consider the rules for the situation in which these interactions can be neglected. That is, von Neumann and Wigner wished … to derive essentially the complete spectroscopic structure of atoms” (Mehra & Rechenberg, *The Historical Development of Quantum Theory*, Vol. 6, pp. 495-6).

“In the [1928] papers of von Neumann and Wigner, the whole apparatus of group characters and representations was put into action and the complete system of term zoology, including selection rules, intensity formulae [and] Stark effect was developed (Van der Waerden, quoted in *ibid*., p. 488).

Born in Budapest, Wigner began his university career in chemistry at the insistence of his father, who wanted him to work in his tannery business. After one year at the Technical Institute in Budapest he transferred to the Technische Hochschule in Berlin where, alongside his chemistry work, Wigner studied physics and mathematics on his own. He attended the physics colloquium and witnessed first-hand the emerging understanding of quantum mechanics. During his third year in Berlin, Wigner began working at the Kaiser Wilhelm Institute in the suburb of Dahlem, where he met Michael Polanyi, a physical chemist who was also a native of Budapest. Polanyi agreed to be Wigner’s thesis advisor for a doctoral dissertation in chemical engineering that contained the first theory of rates of disassociation and association of molecules. After receiving his doctoral degree in 1925, the twenty-two-year-old Wigner dutifully returned home to Budapest to help his father at the tannery. After just one year, however, he accepted an assistantship set up by Polanyi with the x-ray crystallographer Karl Weissenberg at the University of Berlin. Recognizing Wigner’s fine command of mathematics, Weissenberg assigned him a problem that required an exploration of the elementary aspects of group theory. After a few months, Weissenberg arranged for Wigner to work with Richard Becker, who had recently been given a chair at the university in theoretical physics. In 1927 Becker, in turn, suggested that Wigner work with David Hilbert at the University of Göttingen. But Hilbert became ill and retreated from professional work, leaving Wigner without formal responsibilities. Wigner’s time in Göttingen was hardly unproductive, however … at the suggestion of fellow Hungarian Leo Szilard, Wigner began a book, Group *Theory and Its Application to Quantum Mechanics* (1931), which became famous. By the time he left Göttingen, Wigner had firmly launched a career in science. Not only had he begun the book that would make his name, he had started the line of research that would later lead to his award of the Nobel Prize.

Together five offprints from Zeitschrift für Physik 40 Bd., 7 Heft (1926); 40 Bd., 11/12 Heft (1927); 47 Bd., 3/4 Heft (1928); 49 Bd., 1/2 Heft (1928); 51 Bd., 11/12 Heft (1928). 8vo (229 x 155 mm), pp. 492-500; 883-892; 203-220; 73-94; 844-858. Original printed wrappers, stapled as issued (two holes punched in gutter margins of first two offprints, front wrapper of second offprint soiled).

Item #3704

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Price:
$9,500.00
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