WENTZEL, GREGOR

(b. Düsseldorf, Germany, 17 February 1898; d. Ascona, Switzerland, 12 August 1978)

theoretical physics.

Wentzel’s father, Josef Wentzel, was a lawyer who held a quasi-governmental administrative position at a state bank in one of the provinces of Prussia. He was a man of broad intellect with many and varied interests, among which music and literature were particularly prominent. Wentzel’s mother, Anna Joesten, came from an intellectual family whose male members were usually either physicians or priests. The family’s strong cultural interests contrasted with a rather conservative attitude in matters of religion (Catholic).

On 5 December 1929, having succeeded Schrödinger at the University of Zurich a year earlier, Wentzel married Anna L. Wielich. With their son, Donat, who was born in 1934, the Wentzels became Swiss citizens in 1940. Wentzel was president of the Schweizerische Physikalische Gesellschaft from 1945 to 1947. In 1948 he joined the faculty of the University of Chicago, remaining as professor of physics until 1969; he became a U.S. citizen in 1955. Wentzel was elected to numerous learned societies, including the National Academy of Sciences. A final recognition of his achievements was the award of the Max Planck Medal in 1975.

Wentzel was an eminent teacher both in the classroom and as a dissertation adviser. Among his Ph.D. students were Nicolas Kemmer, Markus Fierz, Valya Bargmann, Res Jost, and Felix Villars. His fame as a teacher and as a researcher is reflected in the temporary appointments he held: in 1930, visiting professor at the University of Wisconsin; in 1947, at Purdue University; in 1949, at Stanford University; in 1951 and 1956, at the Tata Institute, Bombay, India; in 1954, at the University of California; and in 1958, at the European Center for Nuclear Research (CERN).

Wentzel’s education was relatively standard. He attended a gymnasium that emphasized Latin, modern languages, the natural sciences, and mathematics. When he was fourteen, Wentzel had as his physics teacher a candidate for a teaching credential who was particularly enthusiastic about the science of astronomy. He got Wentzel to build a telescope and to observe the planets and the stars. It was this stimulus that aroused his interest in science, an interest that had scarcely existed before. Wentzel went to the University of Freiburg in 1916 with the idea of becoming an astronomer. Since a scientific career usually implied accepting a high school teaching position, and such employment meant less status than the family had enjoyed, his parents did not support his decision.

Wentzel’s university career was interrupted by military service after he had been at Freiburg for a semester and a half. Wentzel served in the German Army from 1917 through 1918. Thereafter he returned to Freiburg and spent another semester and a half there. In the autumn of 1919, Wentzel went to Greifswald. Both at Freiburg and at Greifswald, he studied mostly mathematics. At Freiburg he studied with Alfred Loewy and Oskar Bolza, specializing in analysis and complex variables. At Greifswald he was introduced to “mathematician’s mathematics”: set theory with Felix Hausdorff. Although he liked the course, he was not enthusiastic about this sort of mathematics. He studied physics primarily on his own. His reading of Hermann Weyl’s Raum, Zeit und Materie made a deep impression on him. The one physics course that Wentzel did take at Greifswald was a seminar with Johannes Stark, who was assisted by Rudolf Seeliger. Impressed by Wentzel’s performance, Seeliger suggested to him that he study with the theoretical physicist Arnold Sommerfeld at the University of Munich.

Wentzel arrived at Munich in November 1920 and was admitted to Sommerfeld’s seminar. His first presentation there consisted of a novel derivation of Peter Debye’s work on the dispersion of light by permanent dipoles. Sommerfeld was impressed and accepted him as a Ph.D. student. When Wentzel asked him for a doctoral problem, Sommerfeld indicated to him that X-ray spectroscopy was in a “mess” that he was unable to straighten out. “I am prejudiced,” Sommerfeld told him, “and cannot do anything with it. Perhaps you as a younger man may find a clue, and may be able to make sense out of all these lines that increasing experimental work has produced,” Wentzel succeeded in disentangling the wealth of extant spectroscopic data and clarified the structure of X-ray spectra. He obtained a set of rules governing the level scheme of X-ray line spectra, and much of the terminology still used is due to him. The analysis was in terms of two quantum numbers—later interpreted as orbital (ℓ) and total (j) angular momentum—with the selection rules Δ ℓ = ±1, Δ j = ±1 and 0. This work became Wentzel’s doctoral dissertation.

It was at Munich that Wentzel met Wolfgang Pauli and Werner Heisenberg, who also were students in Sommerfeld’s seminar. He saw a good deal of Pauli, and they were very close friends until Pauli’s death.

In the fall of 1921, having received the Ph.D., Wentzel became an assistant at the Munich Institute, where his main duty was the correction of the problems Sommerfeld assigned in his large lecture course. He simultaneously began work on his Habilitationsschrift, for which he chose the problem of β-scattering. In this work he gave an important criterion for distinguishing single from multiple scattering by successive atoms. His researches between 1922 and 1925, during which time he was an assistant to Sommerfeld and a Privatdozent, were primarily concerned with the interpretation of atomic spectra, in particular the fine structure of hydrogen-like atoms. His accomplishments were highly regarded, and Wentzel spent the fall semester (November 1925–February 1926) in Hamburg, replacing Wilhelm Lenz, who had fallen ill.

After the advent of the new quantum mechanics in 1925, Wentzel’s researches had as their object the attempt to discover how far the familiar methods of the “old” quantum theory could be recaptured or rederived within the new matrix and wave mechanics. In the course of these investigations, he developed what later became known as the WKB (Wentzel-Kramers-Brillouin) method in wave mechanics.

After becoming extraordinary professor at the University of Leipzig in 1926, Wentzel worked on the formulation of the wave mechanical theory of radiation-induced and nonradiative transitions. He gave the first wave mechanical treatment of the photoelectric effect in atoms. This paper contains the iε prescription for the separation of outgoing waves by complex integration along suitable paths. His paper on radiationless scattering contains a formula (independently derived by Dirac, using time-dependent perturbation theory) for the transition rate in terms of the interaction matrix elements that is often referred to as the “Golden Rule”. In 1928, Wentzel succeeded Erwin Schrödinger at the University of Zurich. At the same time, Pauli was called to the Eidgenössische Technische Hochschule, and they made Zurich a world center of theoretical physics.

From 1928 to 1933, a good deal of Wentzel’s efforts were invested in the preparation of the course of lectures he gave at the university. His major production during that period was his masterful review of scattering theory and the application of quantum electrodynamics to radiation processes, which appeared in the 1933 edition of the Handbuch der Physik.

In 1933, Wentzel began attacking the divergence problems plaguing quantum field theory. In a series of important papers he formulated the equations of motion of a classical point electron interacting with its own and external fields in such a way that a finite reaction force resulted; but the extension of these methods to quantum electrodynamics proved unsuccessful. After Hideki Yukawa introduced his meson theory of nuclear forces in 1935, perturbation theory became the customary tool for studying nucleon-nucleon and meson-nucleon interactions. However, these results were of dubious value because these interactions are not weak.

Wentzel devoted most of his researches after 1935 to the question of how to avoid weak coupling perturbation methods in the quantum theory of fields. In 1940 he obtained a strong coupling method for handling mesonic interactions and discovered that in several meson theories, mesons could be bound to nucleons to form isobaric states. Later, a more general version of this strong coupling theory provided a useful model that helped to promote understanding of certain phenomena in meson physics (in particular, the 3–3 resonance in pion-nucleon scattering) as caused by the presence of an isobaric state.

In 1941 Wentzel wrote Einführung in die Quantentheorie der Wellenfelder (published in 1943). It was the text from which an entire generation of post-World War II physicists learned quantum field theory and has become a classic. After he joined the University of Chicago faculty, Wentzel’s researches centered on meson field theory and related problems of high-energy physics. His main interest shifted after 1957 to solid-state physics, particularly the problem of superconductivity. Upon retiring from the University of Chicago in 1970, Wentzel settled in Ascona, Switzerland, where he died.

BIBLIOGRAPHY

I. Original Works. Wentzel’s writings include “Zur Systematik der Roentgenspektren”, in Zeitschrift für Physik, 6 (1921), 84–99, his dissertation; “Eine Schwerigkeit für die Theorie des Kreiselektrons”, ibid., 37 (1926), 911–917; “Zur Theorie des photoelektrischen Effekts”, ibid., 40 (1926), 574–589; “Über strahlungslose Quantesnprünge”, ibid., 43 (1927), 524–530; “Über die Eigenkräfte”, ibid., 86 (1933), 479–494 and 635–645, and 87 (1934), 726–733; “Wellenmechanik der Stoss- und Strahlungsvorgänge”, in H. Geiger and Karl Scheel, eds., Handbuch der Physik, XXIV (Berlin, 1933), 695–784; “Zum Problem des statistischen Mesonfeldes”, in Helvetica acta physica 13 (1940), 269–308; “Zur Hypothese der höheren Proton-Isobaren”, ibid., 14 (1941), 3–20; Einführung in die Quantentheorie der Wellenfelder (Vienna, 1943; repr. Ann Arbor, Mich., 1946), trans. by Charlotte Houtermans and J. M. Jauch as Quantum Theory of Fields (New York, 1949); “Recent Research in Meson Physics”, in Review of Modern Physics, 19 (1947), 1–18; and “Quantum Theory of Fields (Until 1947)”, in Markus Fierz and V. F. Weisskopf, eds., Theoretical Physics in the Twentieth Century (New York, 1960), 48–77.

According to his wife, most of Wentzel’s papers were destroyed. A list of his publications is at the Center for the History of Physics at the American Institute of Physics, New York City. An oral interview of Wentzel, by Thomas S. Kuhn, took place 3–5 February 1964; a record of the minutes of this interview is on microfilm in Sources for the History of Quantum Physics.

II. Secondary Literature. An obituary by V. L. Telegdi is in Physics Today, 31, no. 11 (1978), 85–86. A collection of essays dedicated to Wentzel on his retirement from Chicago is P. G. O. Freund, C. J. Goebel, and Y. Nambu, eds., quanta (Chicago, 1970).

S. S. Schweber