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.

Born’s lecture gave Eckart the impetus to investigate the possible general operator formalism for 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[21] on the subject with Sommerfeld and William V.

[8] 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.

In December 1938 in Germany, Otto Hahn and Fritz Strassmann conducted an experiment which pointed towards the fission of uranium.

In January 1939, Meitner and her nephew Otto Frisch correctly interpreted the experimental results as the fission of uranium.

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.

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.

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.

Eckart contributed to geophysics by linking theoretical hydrodynamic exercises to actual physical properties of water.