In 1920, the University of Göttingen offered Max Born its chair of theoretical physics, which had recently been vacated by Peter Debye. Göttingen was an important centre for mathematics, thanks to David Hilbert, Felix Klein, Hermann Minkowski and Carl Runge, but not so much for physics. This would change. As part of his price for coming to Göttingen, Born wanted Franck to head experimental physics there. On 15 November 1920, Franck became Professor of Experimental Physics and Director of the Second Institute for Experimental Physics, a fully tenured professor ordinarius. He was allowed two assistants, so he brought Hertha Sponer with him from Berlin to fill one of the positions. Pohl, a gifted teacher, headed the First Institute, and handled the lectures. Franck refurbished the laboratory with the latest equipment using funds from his own pocket.
Under Born and Franck, Göttingen was one of the worlds great centres for physics between 1920 and 1933. Although they published only three papers together, Born and Franck discussed every one of their papers with each other. Gaining admittance to Francks laboratory became highly competitive. His doctoral students included Hans Kopfermann, Arthur R. von Hippel, Wilhelm Hanle, Fritz Houtermans, Heinrich Kuhn, , Walter Lochte-Holtgreven and Heinz Maier-Leibnitz. In supervising doctoral candidates, Franck had to ensure that thesis topics were well-defined, and would teach the candidate how to conduct original research, while still staying within the limits of the candidates ability, the laboratorys equipment and the institute's budget. Under his direction, research was carried out into the structure of atoms and molecules.
In his own research, Franck developed what became known as the Franck–Condon principle, a rule in spectroscopy and quantum chemistry that explains the intensity of vibronic transitions, simultaneous changes in electronic and vibrational energy levels of a molecule due to the absorption or emission of a photon of the appropriate energy. The principle states that during an electronic transition, a change from one vibrational energy level to another will be more likely to happen if the two vibrational wave functions overlap more significantly. The principle has since been applied to a wide variety of related phenomena.
For his work during this time period, Franck was elected to the American Academy of Arts and Sciences in 1929.