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Following his doctoral studies, Simon took professorship at Princeton for many years, often working with colleague Elliott H. Lieb on the Thomas-Fermi Theory and Hartree-Fock Theory of atoms in addition to phase transitions and mentoring many of the same students as Lieb.
While in medical school, Llewellyn-Thomas was employed as an Electrical Engineer at the Montreal Neurological Institute where he worked with Carl Jasper and Wilder Penfield, who, at that time were engaged in their pioneering work on mapping the electrical activity of the brain.