Heisenberg entered the University of Munich in the fall of 1920. He had planned to study pure mathematics, but after a disconcerting interview with one of the math professors, Heisenberg turned to theoretical physics. The professor of that subject, Arnold Sommerfeld, immediately recognized the young man's talents and admitted him to his advanced seminar, where Heisenberg soon produced a publishable contribution to the old quantum theory of the atom. Since students entered the university at a level roughly equivalent to the junior year of an American college, their studies were more focused on a specific major and soon corresponded to graduate-level work.
"From Sommerfeld I learned optimism, from the Göttingen people mathematics, and from Bohr physics."
—Heisenberg
Heisenberg received his doctorate from the University of Munich in 1923 in the record time of three years. In 1927 he was appointed professor of theoretical physics in Leipzig at the age of 25 --Germany's youngest full professor. From the time he entered the university in Munich until his appointment as professor in Leipzig, Heisenberg studied and trained in three of the world's leading centers for theoretical atomic physics: Munich, Göttingen, and Copenhagen, and with three of the world's leading atomic theorists: Sommerfeld, Max Born, and Niels Bohr. In Munich Heisenberg also began a life-long friendship with Wolfgang Pauli, an equally brilliant young physicist whose extensive correspondence with Heisenberg and others is one of the cultural treasures of the 20th century.
While Sommerfeld was on leave at the University of Wisconsin, Madison, for the 1922-23 academic year, Heisenberg studied in Göttingen as Max Born's student and personal assistant. He returned to Munich to complete his doctorate, then went back to Göttingen as Born's assistant until the spring of 1926. He received the "habilitation," or qualification to lecture at the university level, in 1924. The support of the Rockefeller Foundation enabled Heisenberg to spend the 1924-25 school year at Bohr's institute in Copenhagen, Denmark. He returned to Göttingen in 1925, where he produced the first breakthrough to quantum mechanics. As quantum mechanics evolved over the next year into a more complete form, Heisenberg began looking for a university teaching position. Being one of the few international visitors to Bohr's institute who became fluent in Danish gave him a advantage when Bohr needed a new assistant in 1926. Although it was not a professorship, Heisenberg seized the opportunity to "learn physics" with Bohr, as he put it. His intensive work with Bohr and others in Copenhagen eventually led to Heisenberg's uncertainty principle and to the "Copenhagen Interpretation" of 1927, the capstone to the foundations of quantum mechanics laid by Heisenberg and others during the 1920s.
"For me personally Göttingen has the great advantage that for once I will learn proper mathematics and astronomy."
—Heisenberg, writing to his father, 1922.
Heisenberg's travels and the teachers he encountered during the early 1920s helped him to become one of the leading physicists of his time. But Heisenberg also had the good fortune of entering atomic physics at just the right moment for a breakthrough. At that time the first draft of a revolutionary theory of the atom, the old quantum theory established earlier by Bohr and Sommerfeld, was beginning to break down. Although this theory worked well in simple cases, by the early 1920s when Heisenberg entered the scene, closer experimental and theoretical study was revealing so many problems that some physicists began to speak of a crisis in quantum theory.
German society at that time was also experiencing a crisis. Assassinations and attempts to overthrow the government were frequent. These culminated in November 1923 in the "beer hall putsch," Hitler's failed attempt to seize control of the Bavarian government and military as a prelude to marching on Berlin. At the same time the inflation rate in Germany reached astronomical proportions, rendering the German mark practically worthless. Even after the mark was stabilized in 1924, it was difficult for academics to make a living. Senior German scientists managed to raise private funds from American foundations and philanthropists, which enabled promising young people to remain in the profession through postdoctoral grants. Such funds were Heisenberg's main source of support during this period.
"Not only new assumptions in the usual sense of physical hypotheses will be necessary, but also the entire system of concepts of physics must be rebuilt from the ground up."
—Max Born in 1923
From the very start Heisenberg demonstrated his talent for atomic physics and his ability to leap to the solution of a problem that others were unable to solve. In most cases, however, his solution required the violation of accepted principles and procedures that were later found to be acceptable after all. This was evident in his first paper published as early as 1922. After learning basic physics with Sommerfeld in Munich, in Göttingen Heisenberg learned to follow the physics principles more closely and to apply sophisticated mathematical methods to calculate the hypothetical orbits of the electrons in atoms according to the "old quantum theory." However, the properties of atoms that Heisenberg and Born predicted from the calculations did not agree with existing experimental data. The old quantum theory had failed, but now Heisenberg and his colleagues saw exactly where it failed, and they gained hints for how it might be fixed.