CARL HENRY ECKART May 4,1902-October 23,1973

NATIONAL ACADEMY OF SCIENCES C A R L H E N R Y E CKART 1902—1973 A Biographical Memoir by W A L T E R H . M U N K A N D RU D O L P H W . P REISENDORFER Any opinions expressed in this memoir are those of the author(s) and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 1976 NATIONAL ACADEMY OF SCIENCES WASHINGTON D.C. CARL HENRY ECKART May 4,1902-October 23,1973 BY WALTER H. MUNK AND RUDOLPH W. PREISENDORFER ARL ECKART was a major participant in the development of C quantum mechanics and atomic physics. At the age of forty, with the advent of World War II, he turned his attention to underwater acoustics and related problems in geophysical hydro- dynamics; this was to remain Eckart's primary interest for the rest of his life. His contributions to physics and oceanography are about equally divided. For ten years he directed the Uni- versity of California Division of War Research and its successor, the Marine Physical Laboratory. For two years he was Director of the Scripps Institution of Oceanography. A shy man, he dis- charged these responsibilities with precision, elegance, and gentle care. Carl Eckart, an only child and the son of conservative people of German heritage, was born in St. Louis, Missouri. During his high school years in St. Louis, Eckart's interests were in science and mathematics. These interests, along with an innate ability in fine draftsmanship, left little time for social pursuits. Upon graduation he was awarded a full scholarship to Washington University, in St. Louis, where he received B.S. and M.S. degrees with a major in engineering. Eckart's intention was to turn his interest to mathematics, but this changed to physics, evidently under the influence of Arthur Holly Compton, a physics faculty member (later Chancellor). Compton influenced Eckart to con- 195 196 BIOGRAPHICAL MEMOIRS tinue graduate work at Princeton University, where he went on an Edison Lamp Works Research Fellowship and received a Ph.D. in 1925. It was during this period that Eckart produced his first recorded research paper (with G. E. M. Jauncey) sug- gesting an extension of Compton's classic photon-scattering ex- periment to X rays in crystal lattices. Other papers in this period followed (jointly with Arthur's older brother Karl): a study of low-voltage arcs, particularly the oscillatory phenomena arising in the diffusion of electrons against low-voltage fields. He con- tinued this work as National Research Council Fellow at the California Institute of Technology from 1925 to 1927. During the winter of 1925, Max Born came to Pasadena and gave a lecture on quantum mechanics. This lecture aroused Eckart's interest in a possible general operator formalism for quantum mechanics. Working through the winter of 1925-1926, Eckart developed the formalism and completely familiarized himself with what is now known as the Schrodinger energy operator. In January 1926, when Schrodinger's first paper (of the famous set of four) on wave mechanics appeared in the Annalen der Physik, Eckart immediately recognized its revolu- tionary content. There was, in particular, the puzzling presence of another formulation alternative to Schrodinger's wave mechanics: the matrix mechanics of Heisenberg, which used not the partial differential equation for matter waves, but rather infinite-ordered matrices. Despite their outwardly different struc- ture, the theories yielded identical predictions of atomic spectra and identical relations between atomic constants. Evidently, they were equivalent ways of viewing the same physical phenomena, and Eckart felt that there should be a general mathematical framework that would encompass both formalisms as alternative representations. Working in relative isolation in California, far from the exciting German scientific centers, Eckart soon found the connecting link between the Hilbert space of eigenfunctions of Schrodinger's equation and the CARL HENRY ECKART 197 matrices of the Jordan-Born matrix algebra (which lay at the base of Heisenberg's mechanics). Eckart's solution was submitted to the Proceedings of the National Academy of Sciences on May 31, 1926. But the credit generally went to Schrodinger, whose note to the Annalen der Physik containing essentially the same solution was dated March 18. Later that year, in June 1926, Eckart completed his general study of the operator calculus (see the "note in proof" appended to his paper in Physical Review). This near miss was a source of disappointment for Carl; on the few occasions when a friend could approach him on the subject, he would comment on his isolation in 1926 from the main- stream of quantum physical activity.* But this was soon to change. In 1927, Eckart received a Guggenheim Fellowship to study with Arnold Sommerfeld in Munich. Here he worked on the quantum mechanical behavior of simple oscillators using Schrodinger's equation, developing further the operator calculus that would allow rapid and almost mechanical manipulations of the newly discovered matrix mechanics and gaining new insights into the correspondence prin- ciple. Applications were made to the electron theory of metallic conduction using Fermi statistics, with particular attention to the Volta effect. The German fellowship coincided with the culmination of the twenty-year search by European physicists for the key insights that would consolidate the long series of experimental and theoretical advances in the "old" quantum mechanics begun in 1905 by Planck. The search came to an end in the period 1925-1928 with the advent of Heisenberg's matrix mechanics and Schrodinger's wave mechanics. As we saw, Eckart was an integral part of these exciting developments. During his Ger- * For further discussion of this period of time, see M. Jammer, The Concep- tual Development of Quantum Mechanics (New York: McGraw-Hill Book Co., 1966), p. 275. (We have used the above-cited communication dates as they appear in the original papers.) 198 BIOGRAPHICAL MEMOIRS man fellowship, Eckart became ever more deeply absorbed in the mathematics of the period, which was miraculously made available and compiled for quantum physicists in almost fully developed form* by the applied and pure mathematics schools at Gottingen headed by Felix Klein and David Hilbert. It was this mathematics that would guide Carl Eckart's approaches to all his subsequent theoretical investigations. On his return to the United States in 1928, Eckart was ap- pointed to an Assistant Professorship in the Physics Department at the University of Chicago. Although once again removed from the physics centers of Munich and Gottingen, Eckart con- tinued his quantum mechanical studies over the subsequent fourteen-year period. Particularly noteworthy is the paper (with H. Honl) on the foundations of wave mechanics, an exposition of the role of group theory in the quantum dynamics of mon- atomic systems, and the comparisons of the nuclear theories of Heisenberg and Wigner. It was in this period that Eckart built on his formulations of the so-called Wigner-Eckart theorem, a link between the symmetry transformation groups of space (applied to the Schrodinger equations) and the laws of conserva- tion of energy, momentum, and angular momentum.f It is of practical use in atomic spectroscopy. These researches went hand in hand with teaching activities and with a translation (together with F. C. Hoyt) of Heisenberg's tract on the Physical Principles of Quantum Theory. In all, the decade of the 1930s saw twenty important papers by Eckart in quantum physics. Eckart's paper on the electrodynamics of material media (in 1938) suggests a transition in his interests. By that time he had begun to lose interest in the submicroscopic world of matter * H. Weyl, "David Hilbert and His Mathematical Work," Bulletin of the American Mathematical Society 50(1944):612 (the section on integral equations). f The basic idea occurs in E. P. Wigner, "Some Consequences for Term Struc- ture from Schrodinger's Theory," Zeitschrift fiir Physik 43(1927):624. The idea was elaborated in Eckart's 1930 group theory paper. Our description covers only the simpler cases. For a fuller description, see P. Roman, Advanced Quantum Theory (Reading, Mass.: Addison-Wesley Publishing Co., Inc., 1965), p. 583. CARL HENRY ECK.ART 199 waves. Perhaps he felt that the trend of quantum mechanical research into atomic systems was toward less-rigorous and only partial analyses of solutions of the associated Schrodinger equations. Physicists, facing the complicated multiple interactions of electron systems in the heavier atoms, were adopting simpli- fied models (such as the shell and liquid drop model) that could only partially describe the physical facts. On the other hand, such venerable subjects as electrodynamics and thermodynamics, worked over as they were by several generations of physicists, still contained obscurities and curious gaps between the pure and applied levels. For example, the thermodynamic basis of heat transport and the mechanism of mixing of fluids needed attention. The title of the 1938 paper is somewhat misleading, for it implies a reworking of the Minkowski or Lorentz formulations of the subject. In fact, Eckart achieved a unified theory of Maxwellian and quantum electromagnetics, leading to a gauge- invariant formulation of electrodynamics (previously attempted notably by Mie and Weyl, but without success). He was not successful in extending the formulation to contain as special cases Schrodinger's, Heisenberg's, and Dirac's equations of electrodynamics, but his approach did yield equations closely re- sembling these famous equations and also portions of gas theory for irrotational motion. This latter feature may seem somewhat incongruous, but it falls out quite naturally from a general approach that postulates a set of moving particles of matter characterized by "states" that can be electric, magnetic, or of other forms.

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