After a brilliant performance on his final gymnasium examinations (

During his three years of university study Heisenberg attended Sommerfeld's lectures covering any field of theoretical physics, including the quantum and relativity theories, as well as the special lectures offered by Karl Herzfeld. He showed less interest in the lectures and laboratory exercises in experimental physics provided by Wilhelm Wien. For one of his two minors he attended mathematics courses offered by Lindemann, Alfred Pringsheim, Artur Rosenthal and Aurel Voss. For his second minor he studied astronomy with Hugo von Seeliger.

In Sommerfeld's

In June 1922 Sommerfeld brought his star pupil to Göttingen where Niels Bohr presented a series of lectures on quantum theory and atomic structure – the “Bohr Festival” (12-22 June 1922). There Heisenberg met the leading representatives of atomic physics in Germany and Europe, among them Max Born, Paul Ehrenfest, James Franck, Hendrik Anthony Kramers and Alfred Lande. Bohr and Born began to take notice of the young physicist. When Sommerfeld left for a guest professorship at the University of Wisconsin, Madison, during the winter of 1922/23, Born invited Heisenberg to Göttingen as his personal assistant (November 1922 – March 1923). In Göttingen Heisenberg learned the rigorous mathematical methods of the Hilbert school and worked with Born on the many-body problem in atomic theory, especially on the energy states of the helium atom.

During the summer semester of 1923 Heisenberg completed his dissertation in Munich. In it he successfully treated the problem of the onset of turbulence, which had resisted all previous efforts made by mathematicians and physicists. Sommerfeld was very pleased with this result and the mathematical methods Heisenberg employed. However, Wilhelm Wien, the examiner in experimental physics, came to quite a different conclusion in his field during the final orals (on 23 July 1923) and wanted to fail the candidate. Heisenberg thus received his doctorate “cum laude” rather than “magna” or “summa cum laude”, the two highest marks. In October 1923 Heisenberg became Born's assistant at the University of Göttingen. He continued to work with Born on atomic and molecular models. By means of a modification of the Bohr-Sommerfeld quantum rules he obtained certain advances in the expIanation of the anomalous Zeeman effect. He got his

Heisenberg made his first visit to Bohr's institute in Copenhagen during the spring of 1924 (15 March to early April). With the help of a Rockefeller fellowship (International Education Board) he resided in Copenhagen during the seven months from middle of September 1924 to early April 1925, and during the fall of 1925 (September-October), and otherwise returned to Born's institute in Göttingen. At Bohr's institute Heisenberg met a number of talented young physicists from a variety of nations, among them Christian Møler (Denmark), Svein Rosseland (Norway), G.H. Dieke (Holland), Ralph Fowler (England), Ralph de Laer Kronig and David Dennison (both from U.S.A.). During his visits he learned to speak Danish and English and worked intensively with Bohr and his closest collaborator Kramers on the most difficult problem of atomic theory. This work led to Heisenberg's papers on resonance fluorescence (submitted in November 1924), the dispersion of light by atoms (with Kramers, December 1924) and the structure of complex spectra and their Zeeman effects (April 1925).

During his years of study and postdoctoral research Heisenberg had received in Munich and Göttingen with Sommerfeld and Born a thorough education in all aspects of theoretical physics, while simultaneously familiarizing himself with the main problems of atomic and quantum theory. With Bohr in Copenhagen he deepened his understanding of the foundations of quantum physics. As his friend Pauli wrote (to Kramers on 27 July 1925), Heisenberg “learned a little of philosophical thinking” and moved “noticeably away from the purely formal”. Heisenberg himself later summarized the influence of his teachers thus: “From Sommerfeld I learned optimism, from the Göttingen people mathematics, and from Bohr physics”.

*Abitur*), for which he was accepted as a scholar of the prestigious Maximilianeum Foundation, Heisenberg entered the University of Munich during the winter semester of 1920/21. At first he planned to study pure mathematics, but a discomforting meeting with the famous professor of that subject, Ferdinand von Lindemann, resulted in his turning to theoretical physics. Arnold Sommerfeld, professor of that field, immediately recognized his talents and admitted him to his*Seminar*, composed of advanced students and postdoctoral researchers. Among the*Seminar*members at that time were Gregor Wentzel and Wolfgang Pauli. Otto Laporte and Karl Bechert arrived a little later.During his three years of university study Heisenberg attended Sommerfeld's lectures covering any field of theoretical physics, including the quantum and relativity theories, as well as the special lectures offered by Karl Herzfeld. He showed less interest in the lectures and laboratory exercises in experimental physics provided by Wilhelm Wien. For one of his two minors he attended mathematics courses offered by Lindemann, Alfred Pringsheim, Artur Rosenthal and Aurel Voss. For his second minor he studied astronomy with Hugo von Seeliger.

In Sommerfeld's

*Seminar*Heisenberg studied the latest literature in physics and carried on intensive discussions of the problems arising from it with his teacher and a group of excellent fellow students. Under Sommerfeld's direction he delved into the problems of atomic theory, a difficult and abstract discipline that tended to attract the best and most dedicated young theorists of the day. As early as his first semester Heisenberg presented a quantum-theoretical analysis of the anomalous Zeeman effect, the results of which he utilized a year later in his first publication (submitted in November 1921). At the same time he examined problems in hydrodynamics, a subject on which he published his second paper (on Kármán vortices, 1922) held his first public lecture in September 1922 (at a topical conference in Innsbruck), and wrote his doctoral dissertation (finished in July 1923).In June 1922 Sommerfeld brought his star pupil to Göttingen where Niels Bohr presented a series of lectures on quantum theory and atomic structure – the “Bohr Festival” (12-22 June 1922). There Heisenberg met the leading representatives of atomic physics in Germany and Europe, among them Max Born, Paul Ehrenfest, James Franck, Hendrik Anthony Kramers and Alfred Lande. Bohr and Born began to take notice of the young physicist. When Sommerfeld left for a guest professorship at the University of Wisconsin, Madison, during the winter of 1922/23, Born invited Heisenberg to Göttingen as his personal assistant (November 1922 – March 1923). In Göttingen Heisenberg learned the rigorous mathematical methods of the Hilbert school and worked with Born on the many-body problem in atomic theory, especially on the energy states of the helium atom.

During the summer semester of 1923 Heisenberg completed his dissertation in Munich. In it he successfully treated the problem of the onset of turbulence, which had resisted all previous efforts made by mathematicians and physicists. Sommerfeld was very pleased with this result and the mathematical methods Heisenberg employed. However, Wilhelm Wien, the examiner in experimental physics, came to quite a different conclusion in his field during the final orals (on 23 July 1923) and wanted to fail the candidate. Heisenberg thus received his doctorate “cum laude” rather than “magna” or “summa cum laude”, the two highest marks. In October 1923 Heisenberg became Born's assistant at the University of Göttingen. He continued to work with Born on atomic and molecular models. By means of a modification of the Bohr-Sommerfeld quantum rules he obtained certain advances in the expIanation of the anomalous Zeeman effect. He got his

*Habilitation*at the University of Göttingen on 28 July 1924. Although only 22 years old, he thus became a Privatdozent and fully qualified as a university lecturer.Heisenberg made his first visit to Bohr's institute in Copenhagen during the spring of 1924 (15 March to early April). With the help of a Rockefeller fellowship (International Education Board) he resided in Copenhagen during the seven months from middle of September 1924 to early April 1925, and during the fall of 1925 (September-October), and otherwise returned to Born's institute in Göttingen. At Bohr's institute Heisenberg met a number of talented young physicists from a variety of nations, among them Christian Møler (Denmark), Svein Rosseland (Norway), G.H. Dieke (Holland), Ralph Fowler (England), Ralph de Laer Kronig and David Dennison (both from U.S.A.). During his visits he learned to speak Danish and English and worked intensively with Bohr and his closest collaborator Kramers on the most difficult problem of atomic theory. This work led to Heisenberg's papers on resonance fluorescence (submitted in November 1924), the dispersion of light by atoms (with Kramers, December 1924) and the structure of complex spectra and their Zeeman effects (April 1925).

During his years of study and postdoctoral research Heisenberg had received in Munich and Göttingen with Sommerfeld and Born a thorough education in all aspects of theoretical physics, while simultaneously familiarizing himself with the main problems of atomic and quantum theory. With Bohr in Copenhagen he deepened his understanding of the foundations of quantum physics. As his friend Pauli wrote (to Kramers on 27 July 1925), Heisenberg “learned a little of philosophical thinking” and moved “noticeably away from the purely formal”. Heisenberg himself later summarized the influence of his teachers thus: “From Sommerfeld I learned optimism, from the Göttingen people mathematics, and from Bohr physics”.