Carl Henry Eckart (May 4, 1902 – October 23, 1973) was an American physicist, physical oceanographer, geophysicist, and administrator. He co-developed the Wigner–Eckart theorem and is also known for the Eckart conditions in quantum mechanics,[1] and the Eckart–Young theorem in linear algebra.[2]
Early life
Eckart was born in St. Louis, Missouri. He began college in 1919 at Washington University in St. Louis where he received his B.S. and M.S. degrees with a major in engineering. However, due to Arthur Holly Compton, a physics faculty member and later Chancellor, Eckart was influenced to continue his education in physics at Princeton, where he went in 1923 on an Edison Lamp Works Research Fellowship. Eckart was awarded his Ph.D. in 1925.[3][4][5]
During his graduate studies, Eckart co-authored a paper with Karl Compton,[6] brother of Arthur Compton on low-voltage arcs, particularly the oscillatory phenomena arising in the diffusion of electrons against low-voltage fields. He continued this line of work after receipt of his Ph.D. on a National Research Council Fellowship at the California Institute of Technology (Caltech) during the period 1925 to 1927.[3] Max Born, Director of the Institute for Theoretical Physics at the University of Göttingen and co-developer of the matrix mechanics formulation of quantum mechanics with Werner Heisenberg,[7] came to Caltech in the winter of 1925 and gave a lecture on his work. Born’s lecture gave Eckart the impetus to investigate the possible general operator formalism for quantum mechanics. Working into early 1926, Eckart developed the formalism. When Erwin Schrödinger’s first paper[8] in the series of four[9][10][11] on the wave mechanics formulation of quantum mechanics was published in January, Eckart soon realized that the matrix formulation and wave formulation of quantum mechanics were equivalent; he submitted his paper[12] to the Proceedings of the National Academy of Sciences of the United States of America for publication. However, it was communicated on May 31, 1926, and Schrödinger’s paper[13] on the equivalence was received on March 18, 1926, thus giving him credit for the realization.[3] In 1927 Eckart received a Guggenheim Fellowship to do postdoctoral study and research with Arnold Sommerfeld at the Ludwig Maximilian University of Munich, one of the three main centers for the development of quantum mechanics, the others being Göttingen under Born and the University of Copenhagen under Niels Bohr. Also at Munich simultaneous with Eckart were Rudolf Peierls, and two other Guggenheim Fellows, Edwin C. Kemble and William V. Houston.[14][15] In Munich, Eckart worked on the quantum mechanical behavior of simple oscillators using the Schrödinger equation and on operator calculus related to the matrix formulation of quantum mechanics. He also applied his work to the theory of electrons and the conductivity of metals using Fermi statistics, and he co-authored a paper[16] on the subject with Sommerfeld and William V. Houston.[3]
Career
University of Chicago
Returning to the United States in 1928, Eckart was appointed Assistant Professor in the Physics Department at the University of Chicago, where he continued his work on quantum mechanics for another 14 years. Noteworthy was a paper co-authored with Helmut Hönl, who received his doctorate under Sommerfeld in 1926; the paper, on the foundations of quantum mechanics, dealt with the role of group theory in quantum dynamics in monatomic systems and comparisons of the nuclear theories of Werner Heisenberg and Eugene Wigner. During this period, Eckart developed his formulation of the Wigner-Eckart theorem – a link between symmetry transformation groups applied to the Schrödinger equation and the laws of conservation of energy, momentum, and angular momentum. The theorem is particularly useful in spectroscopy. With F. C. Hoyt, Eckart translated[17] Heisenberg’s book on the physical principles of quantum mechanics. During the 1934-1935 academic year, Eckart took a sabbatical at the Institute for Advanced Study in New Jersey, as he also did in the academic years 1952-1953 and 1960-1961.[3][4] During this period he published, along with Gale Young, a proof of the Eckart-Young theorem, which solves the problem of least-squares approximation of a given matrix by a matrix of lower rank.
In December 1938 in Germany, Otto Hahn and Fritz Strassmann conducted an experiment which pointed towards the fission of uranium. They communicated their results to their former colleague Lise Meitner, who had fled Germany earlier in the year. In January 1939, Meitner and her nephew Otto Frisch correctly interpreted the experimental results as the fission of uranium. News of the discovery spread very rapidly. With the potential of making a fission-based atomic weapon and the threat of war in Europe, this caused anxiety in many, Leó Szilárd for example, that Germany would develop an atomic weapon. As a result of two meetings with Albert Einstein, the first with Szilárd and Eugene Wigner and the second with Szilárd and Edward Teller, Einstein signed the Einstein–Szilárd letter to President Franklin Delano Roosevelt (FDR) in August. World War II broke out in Europe in September. The letter was delivered to FDR in October by economist and banker Alexander Sachs. In response to the letter, the Uranium Committee was formed that month. The Committee was organized into subsections by topic. The Theoretical Aspects Subsection, chaired by Enrico Fermi, was located at the University of Chicago, and Eckart was a member of it.[18] However, in 1941, Eckart withdrew from the Committee because of his anti-atomic bomb sentiments.[3][4] Also notable during this period are his papers on the thermodynamics of irreversible processes.
University of California, San Diego
With the entry of the United States into WW II in December 1941, there was increased incentive for the scientific community to participate in the war effort. Axis submarines were exacting a toll on allied shipping, and university scientists were being approached by the U. S. Navy concerning optical and acoustical detection of submarines. B. O. Knudsen, director of the newly formed University of California Division of War Research, and his associate L. P. Delsasso approached Eckart for help. Eckart (an Associate Professor) took leave from the University of Chicago to work on the problem, thus beginning his 31-year stay in California. From 1942, he was assistant director of the Division of War Research, and eventually he was director, a position he held until 1946.[3][4]
In 1946, Eckart officially resigned his position at the University of Chicago to become a professor of geophysics at the Scripps Institution of Oceanography of the University of California, San Diego (UCSD), a position he held until 1971. In 1946 he also became the first director of the Marine Physical Laboratory (MPL) of the University of California. The MPL was founded by Eckart, Roger Revelle, and Admiral Rawson Bennett to conduct geophysical research of common interest to the academic and naval communities. In 1948, the MPL became an integral part of the Scripps Institution of Oceanography, and Eckart served as the fourth director of Scripps until 1950. Eckart contributed to geophysics by linking theoretical hydrodynamic exercises to actual physical properties of water. In the following decades he did research on thermal layering in the ocean and atmospheres on which he wrote a book, the transmission of sound in the sea, turbulence, air-sea interactions, the generation and structure of surface, and internal ocean waves.[3][4]
After WW II, Eckart collected his work and the work of others on underwater detection and published it a classified volume entitled Principles and Applications of Underwater Sound, which was first published in 1946. It was declassified in 1954 and reprinted in 1968. It is a standard reference.[3]
During the period 1957 to 1959, Eckart was a member of the Editorial Advisory Board for the Johns Hopkins University Applied Physics Laboratory’s series on applied mathematics and mechanics. From 1959 through 1970, he was also a consultant for commercial enterprises such as General Dynamics Corporation and the Rand Corporation.[4]
From 1965 to 1967, Eckart was vice-chancellor for academic affairs at UCSD. He then served the University of California, from 1967 to 1968, as alternate representative to the Institute for Defense Analyses, which was made up of 12 member universities and functioned as an independent source for studies and advice for the Department of Defense.[4]
Eckart contributed to the posthumous publication of some works by the mathematician John von Neumann.[4]
Personal life
Eckart married Edith Louise née Frazee in 1926; they were divorced in 1948. In 1958, he married Klara Dan von Neumann, the widow of the mathematician John von Neumann; Klara died in 1963 in a drowning accident, officially ruled a suicide.[3][4] Eckart himself died in La Jolla, California.
Honors
1948 – Certificate of Merit signed by President Harry Truman
1952 – Elected to the National Academy of Sciences
1966 – Awarded the Alexander Agassiz Medal by the National Academy of Sciences for contributions to oceanography.
1972 – Awarded the William Bowie Medal by the American Geophysical Union for outstanding contributions to fundamental geophysics.
Books
Werner Heisenberg, Translated by Carl Eckart and F. C. Hoyt The Physical Principles of the Quantum Theory (Dover, 1930)
Carl Eckart and others. Principles and Applications of Underwater Sound (NRDC, 1946). Originally a classified document and published as a Summary Technical Report of Division 6, NDRC Volume 7, Washington, D.C., 1946. Declassified and distributed September 7, 1954. Reprinted and redistributed by Department of the Navy Headquarters Naval Material Command, Washington, D.C., 1968.[3][19]
Carl Eckart Hydrodynamics of Oceans and Atmospheres (Pergamon Press, 1960)[20]
Selected literature
Carl Eckart The Solution of the Problem of the Simple Oscillator by a Combination of the Schrödinger and the Lanczos Theories, Proceedings of the National Academy of Sciences of the United States of America 12 473-476 (1926). Submitted 31 May 1926. doi:10.1073/pnas.12.7.473
Carl Eckart (National Research Fellow) Operator Calculus and the Solution of the Equations of Quantum Dynamics, Phys. Rev. 28 (4) 711 - 726 (1926). California Institute of Technology. Received 7 June 1926. doi:10.1103/PhysRev.28.711
A. Sommerfeld, W. V. Houston, and C. Eckart, Zeits. f. Physik 47, 1 (1928)
Carl Eckart The Application of Group theory to the Quantum Dynamics of Monatomic Systems, Rev. Mod. Phys. 2 (3) 305 - 380 (1930). University of Chicago. doi:10.1103/RevModPhys.2.305
Carl Eckart, Some Studies Concerning Rotating Axes and Polyatomic Molecules, Physical Review 47 552-558 (1935). doi:10.1103/PhysRev.47.552
Carl Eckart The Approximate Solution of One-Dimensional Wave Equations, Rev. Mod. Phys. 20 (2) 399 - 417 (1948). University of California, Marine Physical Laboratory, San Diego, California. doi:10.1103/RevModPhys.20.399
See also
Eckart Hamiltonian
References
Wikiquote has quotations related to Carl Eckart.
Arnold Sommerfeld Some Reminiscences of My Teaching Career, American Journal of Physics 17 (5) 315-316 (1949)
Notes
C. Eckart, Some studies concerning rotating axes and polyatomic molecules, Physical Review 47 552-558 (1935).
C. Eckart and G. Young, The approximation of one matrix by another of lower rank, Psychometrika 1(3) 211-218 (1936). doi:10.1007/BF02288367
Eckart Biography Archived 2007-03-25 at the Wayback Machine – The National Academies Press
Eckart Papers – Library of Congress
Author Catalog: Eckart Archived February 5, 2007, at the Wayback Machine – American Philosophical Society
K. T. Compton and Carl Eckart The Diffusion of Electrons Against an Electric Field in the Non-Oscillatory Abnormal Low Voltage Arc, Phys. Rev. 25 (2) 139 - 146 (1925). Palmer Physical Laboratory, Princeton, New Jersey, Received 29 October 1924.
Heisenberg was granted his doctorate under Arnold Sommerfeld at the Ludwig Maximilian University of Munich in 1923 and completed his Habilitation under Max Born at the University of Göttingen in 1924.
Erwin Schrödinger (From the German) Quantization as an Eigenvalue Problem (First Communication), Annalen der Physik 79 (4) 361-376, 1926. [English translation in Gunter Ludwig Wave Mechanics 94-105 (Pergamon Press, 1968) ISBN 0-08-203204-1]
Erwin Schrödinger (From the German) Quantization as an Eigenvalue Problem (Second Communication), Annalen der Physik 79 (6) 489-527, 1926. [English translation in Gunter Ludwig Wave Mechanics 106-126 (Pergamon Press, 1968) ISBN 0-08-203204-1]
Erwin Schrödinger (From the German) Quantization as an Eigenvalue Problem (Third Communication), Annalen der Physik 80 (13) 437-490, 1926.
Erwin Schrödinger (From the German) Quantization as an Eigenvalue Problem (Fourth Communication), Annalen der Physik 81 (18) 109-139, 1926. [English translation in Gunter Ludwig Wave Mechanics 151-167 (Pergamon Press, 1968) ISBN 0-08-203204-1]
Eckart Paper – Carl Eckart The Solution of the Problem of the Simple Oscillator by a Combination of the Schrödinger and the Lanczos Theories, Proceedings of the National Academy of Sciences of the United States of America 12 473-476 (1926). California Institute of Technology. Communicated May 31, 1926.
Erwin Schrödinger Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen (Translated from the German: On the Relationship of the Heisenberg-Born-Jordan Quantum Mechanics to Mine) Annalen der Physik 79 (8) 734-756, 1926. Received March 18, 1926. [English translation in Gunter Ludwig Wave Mechanics 127-150 (Pergamon Press, 1968) ISBN 0-08-203204-1]
Arnold Sommerfeld Some Reminiscences of My Teaching Career, American Journal of Physics 17 (5) 315-316 (1949)
Sommerfeld Biography Archived September 27, 2006, at the Wayback Machine – American Philosophical Society
A. Sommerfeld, W. V. Houston, and C. Eckart, Zeits. f. Physik 47, 1 (1928)
Werner Heisenberg, Translated by Carl Eckart and F. C. Hoyt The Physical Principles of the Quantum Theory (Dover, 1930)
Uranium Committee
"DTIC". Archived from the original on 2011-07-22. Retrieved 2007-02-03.
Gillis, J. (1961). "Review of Hydrodynamics of Oceans and Atmospheres by Carl Eckart". Physics Today. 14 (8): 52. doi:10.1063/1.3057700. ISSN 0031-9228.
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