# Eckart, Carl Henry

# ECKART, CARL HENRY

(*b*. St. Louis, Missouri, 4 May 1902; J. La Jolla, California, 23 October 1973)

*physics, geophysics, acoustics*.

Eckart was the son of William Eckart and Lilly Hellwig Eckart. After receiving the B.S. in engineering from Washington University (St. Louis) in 1922, he held a one-year fellowship for graduate work there, studying under George E. M. Jauncey and receiving a master’s degree in 1923. For the next two years he studied under Karl T. Compton at Princeton, supported by an Edison Lamp Works fellowship, and received the Ph.D. in 1925. In order to work with Paul S. Epstein, Eckart moved to the California Institute of Technology, where he held a National Research fellowship. Eckart’s first marriage (1926) ended in divorce after eighteen years. He was married again in 1958 to Klara von Neumann, the widow of a friend of his, the mathematician John von Neumann; she drowned in 1963. Both marriages were childless.

A Guggenheim fellowship enabled Eckart to work with Arnold Sommerfeld at Munich in the academic year 1927–1928. In the latter year he returned to the United States and became assistant professor of physics at the University of Chicago. From 1931 to 1946 Eckart was associate professor at Chicago, and from 1942 to 1946 he was assistant director (and then director) of the University of California’s division of war research at San Diego. In 1946 he became professor of geophysics at the University of California, Los Angeles. He served as director of the Marine Physical Laboratory. San Diego, from 1946 to 1952; from 1948 (when the Marine Physical Laboratory became an integral part of the Scripps Institution of Oceanography at the University of California. La Jolla) he was also at this latter institution, serving as director from 1948 to 1950; Eckart was vice chancellor for academic affairs at the University of California, San Diego, from 1965 to 1969, He retired in 1971.

The greatest influence on Eckart’s scientific career was Frank W. Bubb, professor of applied mathematics at Washington University. Working with Bubb. Eckart became acquainted with descriptive geometry, vector analysis, and the elements of theoretical physics. Ironicnlh. although he planned to do graduate work in mathematics, only his application for a teaching fellowship in the physics department, where Bubb had prepared the ground, was successful.

When Eckart started graduate work with George E. M. Jauncey at Washington University. he was immediately involved in the ongoing discussions between Jauncey and Arthur H. Compton on the scattering of X rays and gamma rays. Although these discussions were very important for Compton’s development of the quantum theoretical explanation of the greater coefficient of absorption of gamma rays, the X-ray experiments, which eventually led to the establishment of the Compton effect, were entirely the work of Compton alone. Jauncey and Eckart only performed experiments to confirm the assumption that the modified radiation is incoherent and thus does not produce any interference effects.

Clearly under the influence of Louis de Broglie’s wave theory of the electron, which stressed the similarity of a trajectory of a particle and the normal to a wave front, Eckart tried to give a different explanation of the Compton effect by deriving the change in frequency from the calculation of a curved path of an electromagnetic wave in the nonstatic gravitational field of the recoil electron. In 1925, when Max Born lectured at Prasadena, Eckart’s interest in the new quantum mechanics was stimulated. Another influence came from Cornel Lanczos, who in 1925 had shown that the Heisenberg-Born-Jordan theory can be expressed not only in terms of matrices but also in terms of integral equations.

Eckart therefore spent the spring of 1926 using the operator calculus to connect the already published Heisenberg-Born-Jordan matrix mechanics and Erwin Schrödinger’s wave equation, which has easily intelligible quantum conditions. Deriving the matrices by integrations of the orthonormal eigenfunctions (of the “characteristic” solutions) of the wave equation, he solved the problem in the case of the harmonic oscillator. His result was partly worked out and presented in a preliminary paper submitted to *Proceedings of the National Academy of Sciences* on 31 March 1926. However, Schröedinger, in a paper received by the editor of *Annalen der Physik* on 18 March 1926, had already clarified the relation between the quantum mechanics of Heisenberg, Born, and Jordan and that of Schrödinger. Due to delay in the mails, Eckart’s preliminary paper was published before Schrödinger’s paper reached him at Caltech. Thus, in his completed paper in *Physical Review*, Eckart had to acknowledge Schrödinger’s priority.

Although theoretical physics in the united States matured around 1925, postdoctoral work in Germany was still very attractive. Eckart and William Houston worked with Arnold Sommerfield at Munich, arriving just in time to be involved in the electron gas theory of metals, which was reformulated by Sommerfeld and his school the help of Fermi statistics; Eckart dealt with special problems of contact phenomena and with thermionics. Later, in Berlin, he had a disappointing encounter with John von neumann’s completely abstract approach to quantum theory and with Schrödinger’s search for a representation in easily visualizable three-dimensional space. When Eckart returned to the United States in 1928 and joined the staff of the physics department at the University of Chicago, his work remained in the realm of quantum theory. With Helmut Hönl he wrote an overview article for *Physikalische Zeitschrift* on the principles and results of wave mechanics, and with Frank C. Hoyt he prepared the English edition of Werner Heisenberg’s *Physical Principles of Quantum Theory*, lectures that had been delivered in 1929.

Eckart stressed the importance of the statistical interpretation and the linguistic character of the uncertainty principle. His (and Eugen P.Wigner’s) work on the application of group theory in quantum theory led to the Wigner-Eckart theorem, which is a means to calculate the resulting angular momenta of complex systems in quantum theory.

Beginning in 1930, Eckart did research in diffraction by gratings, the quantum theory of polyatomic molecules, the theories of the atomic nucleus, and cosmic ray measurements. In the 1940’s he focused on the thermodynamics of fluids, on geophysical hydrodynamics, and on wave generation and propagation in fluids. The latter topics were closely related to the development of sonar systems at the University of California division of war research, so his report. “The Principles of Underwater Sound,” was only declassified in 1954.

In underwater acoustics Eckart concentrated on the theory of reverberation and scattering of sound from the sea surface. With better approximations he tried to make the available data for short wave sound an additional source of information for the geometry and the kinematics of the sea surface. Also influential in the sonar field was his research on optimal rectifier systems for detecting steady signals in noise. He continued applying the thermodynamics of irreversible processes to the physics of fluids, to the behavior of elastic and unelastic media, and to oceanic phenomena, especially to surface waves. Starting from a wave equation analogous to Schrödinger’s he contributed to the theory of internal oscillations of the sea.

Although Eckart essentially brought into play the mathematical tools developed earlier in hydrodynamics, in the solution of wave equations, in statistical thermodynamics, and in the “new” quantum mechanics, he often carried his approximations to such a degree that his analysis was valuable in studying actual phenomena. So he encouraged experimental work on the unexplained high absorption shown by seawater as opposed to fresh water, and on the propagation of sound penetrating significantly into the crust of the earth below the sea.

Eckart was a member of the National Academy of Sciences and of the American Academy of arts and Sciences. He received the Agassiz Medal of the National Academy of Sciences for his contribution to the hydrodynamics of the ocean, and the American geophysical Union awarded him the Bowie Medal. On 31 October 1973 the Acoustical Society of America honored him posthumously with the Pioneers of Underwater Acoustics Medal for his contributions to the understanding of underwater sound and acoustic signal processing.

## BIBLIOGRAPHY

I. Original Works. Eckart’s writings include “The Wave Theory of the Compton Effect,” in *Physical Review*, 2nd ser. 24 (1924), 591–596; “Post-Arc Conductivity and Metastable Helium,” *ibid.*. **26** (1925), 454–464, his dissertation; “Operator Calculus and the Solution of the Equations of Quantum Dynamics,” *ibid.*. **28** (1926), 711–726; “Ünder die Elektronentheorie der Metalle auf Grund der Fermischen Statistik, insbesondere über den VoltaEffekt,” in *Zeitschrift für Physik***47** (1928), 38–42; “The Application of Group Theory to the Quantum Dynamics of Monoatomic Systems,” in *Review of Modern Physics*, **2** (1930), 305–380; “Grundzuge und Ergebnisse der Wellenmechanik,” in *Physikalische Zeitschrift***31** (1930), 89–119 145–160, written with Helmut Hönl; *The Physical Principles of the Quantum Theory*, by Werner Heisenberg translated by Eckart and Frank C. Hoyt(Chicago, 1930); and *Hydrodynamics of Oceans and Atmospheres* (NewYork 1960).

“Seminar on Wave Theory,” notes of lectures delivered at the Marine Physical Laboratory, San Diego, in 1946 and 1947 are at the library of the University of California, Berkeley. “Surface Waves on Water of variable Depth,” notes of lectures delivered at the Scripps Institution of Oceanography in 1950 and 1951 were issued as *Wave Report* no. 100 (1951), held at the library of the U.S. Department of the Interior.

Letters to or from Eckart are at Mudd Library, Princeton University; Nathan Marsh Pusey Library, Harvard University; Fondren Library, Rice University; the Deutsches Museum, Munich; Bancroft Library. University of California, Berkeley; and Archive for History of Quantum Physics, Office for History of Science and Technology, University of California, Berkeley. The last also has the transcript of an interview with Eckart, conducted by John L. Heilbron on 31 May 1962. The collected unpublished works of Carl Eckart are at the library of the Scripps Institution of Oceanography, University of California, San Diego.

II. Secondary Literature. A biographical article is Walter H. Munk and Rudolph W. Preisendorfer, “Carl Henry Eckart,” in *Biographical Memoirs. National Academy of Sciences*, **48** (1976), 195–219, with A bibliography of his works. On the Wigner-Eckart theorem see eugen wigner, “Einige Folgerungen aus der Schrodingerschen Theorie fur die Termstrukturen,” in *Zeitschrift für Physik*. **43** (1927), 624–652.

Walter Kaiser

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