Carl Eckart

Carl Henry Eckart (May 4, 1902 in St. Louis, Missouri – October 23, 1973 in La Jolla, California) 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, and the Eckart–Young theorem in linear algebra.

Eckart 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.

During his graduate studies, Eckart co-authored a paper with Karl Compton, 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.Max Born, Director of the Institute for Theoretical Physics at the Georg-August University of Göttingen and co-developer of the matrix mechanics formulation of quantum mechanics with Werner Heisenberg, 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 in the series of four 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 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 on the equivalence was received on March 18, 1926, thus giving him credit for the realization. In 1927 Eckart received a Guggenheim Fellowship to do postdoctoral study and research with Arnold Sommerfeld at the Ludwig Maximilians 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. 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 on the subject with Sommerfeld and William V. Houston.

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