Werner Heisenberg (5 December 1901 – 1 February 1976) was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory. In addition, he made important contributions to nuclear physics, quantum field theory, and particle physics.

Heisenberg, along with Max Born and Pascual Jordan, set forth the matrix formulation of quantum mechanics in 1925. Heisenberg was awarded the 1932 Nobel Prize in Physics. Following World War II, he was appointed director of the Kaiser Wilhelm Institute for Physics, which was soon thereafter renamed the Max Planck Institute for Physics. He was director of the institute until it was moved to Munich in 1958, when it was expanded and renamed the Max Planck Institute for Physics and Astrophysics. Heisenberg was also president of the German Research Council, chairman of the Commission for Atomic Physics, chairman of the Nuclear Physics Working Group, and president of the Alexander von Humboldt Foundation.

Heisenberg was born in Würzburg, Germany to Kaspar Ernst August Heisenberg, a secondary school teacher of classical languages who became Germany's only ordentlicher Professor (ordinarius professor) of medieval and modern Greek studies in the university system and his wife Annie Wecklein.

He studied physics and mathematics from 1920 to 1923 at the Ludwig-Maximilians-Universität München and the Georg-August-Universität Göttingen. At Munich, he studied under Arnold Sommerfeld and Wilhelm Wien. At Göttingen, he studied physics with Max Born and James Franck, and he studied mathematics with David Hilbert. He received his doctorate in 1923, at Munich under Sommerfeld. He completed his Habilitation in 1924, at Göttingen under Born.

In his youth he was a member and Scoutleader of the Neupfadfinder, a German Scout association and part of the German Youth Movement. In August 1923 Robert Honsell and Heisenberg organized a trip (Großfahrt) to Finland with a Scout group of this association from Munich.

Because Sommerfeld had a sincere interest in his students and knew of Heisenberg's interest in Niels Bohr's theories on atomic physics, Sommerfeld took Heisenberg to Göttingen to the Bohr-Festspiele (Bohr Festival) in June 1922. At the event, Bohr was a guest lecturer and gave a series of comprehensive lectures on quantum atomic physics. There, Heisenberg met Bohr for the first time, and it had a significant and continuing effect on him.

Heisenberg's doctoral thesis, the topic of which was suggested by Sommerfeld, was on turbulence; the thesis discussed both the stability of laminar flow and the nature of turbulent flow. The problem of stability was investigated by the use of the Orr–Sommerfeld equation, a fourth order linear differential equation for small disturbances from laminar flow. He would briefly return to this topic after World War II.

Heisenberg's paper on the anomalous Zeeman effect was accepted as his Habilitationsschrift under Max Born at Göttingen.

From 1924 to 1927, Heisenberg was a Privatdozent at Göttingen. From 17 September 1924 to 1 May 1925, under an International Education Board Rockefeller Foundation fellowship, Heisenberg went to do research with Niels Bohr, director of the Institute of Theoretical Physics at the University of Copenhagen. He returned to Göttingen and with Max Born and Pascual Jordan, over a period of about six months, developed the matrix mechanics formulation of quantum mechanics. On 1 May 1926, Heisenberg began his appointment as a university lecturer and assistant to Bohr in Copenhagen. It was in Copenhagen, in 1927, that Heisenberg developed his uncertainty principle, while working on the mathematical foundations of quantum mechanics. In his paper on the uncertainty principle, Heisenberg used the word "Ungenauigkeit" (imprecision).

In 1927, Heisenberg was appointed ordentlicher Professor (ordinarius professor) of theoretical physics and head of the department of physics at the Universität Leipzig; he gave his inaugural lecture on 1 February 1928. In his first paper published from Leipzig, Heisenberg used the Pauli exclusion principle to solve the mystery of ferromagnetism.

In Heisenberg's tenure at Leipzig, the quality of doctoral students, post-graduate and research associates who studied and worked with Heisenberg there is attested to by the acclaim later earned by these personnel. At various times, these personnel included: Erich Bagge, Felix Bloch, Ugo Fano, Siegfried Flügge, William Vermillion Houston, Friedrich Hund, Robert S. Mulliken, Rudolf Peierls, George Placzek, Isidor Isaac Rabi, Fritz Sauter, John C. Slater, Edward Teller, John Hasbrouck van Vleck, Victor Frederick Weisskopf, Carl Friedrich von Weizsäcker, Gregor Wentzel, and Clarence Zener.

In early 1929, Heisenberg and Wolfgang Pauli submitted the first of two papers laying the foundation for relativistic quantum field theory. Also in 1929, Heisenberg went on a lecture tour in the United States, Japan, China, and India.

Shortly after the discovery of the neutron by James Chadwick in 1932, Heisenberg submitted the first of three papers on his neutron-proton model of the nucleus. He was awarded the 1932 Nobel Prize in Physics.

In 1928, the British mathematical physicist P.A.M. Dirac had derived the relativistic wave equation of quantum mechanics, which implied the existence of positive electrons, later to be named positrons. In 1932, from a cloud chamber photograph of cosmic rays, the American physicist Carl David Anderson identified a track as having been made by a positron. In mid-1933, Heisenberg presented his theory of the positron. His thinking on Dirac's theory and further development of the theory were set forth in two papers. The first, Bemerkungen zur Diracschen Theorie des Positrons (Remarks on Dirac's theory of the positron) was published in 1934, and the second, Folgerungen aus der Diracschen Theorie des Positrons (Consequences of Dirac's Theory of the Positron), was published in 1936.

In the early 1930s in Germany, the deutsche Physik movement was anti-Semitic and anti-theoretical physics, especially including quantum mechanics and the theory of relativity. As applied in the university environment, political factors took priority over the historically applied concept of scholarly ability, even though its two most prominent supporters were the Nobel Laureates in Physics Philipp Lenard and Johannes Stark. After Adolf Hitler came to power in 1933, Heisenberg was attacked in the press as a "White Jew" by elements of the deutsche Physik (German Physics) movement for his insistence on teaching about the roles of Jewish scientists. As a result, he came under investigation by the SS. This was over an attempt to appoint Heisenberg as successor to Arnold Sommerfeld at the University of Munich. The issue was resolved in 1938 by Heinrich Himmler, head of the SS. While Heisenberg was not chosen as Sommerfeld's successor, he was rehabilitated to the physics community during the Third Reich. Nevertheless, supporters of deutsche Physik launched vicious attacks against leading theoretical physicists, including Arnold Sommerfeld and Heisenberg. On 29 June 1936, a National Socialist Party newspaper published a column attacking Heisenberg. On 15 July 1937, he was attacked in a journal of the SS. This was the beginning of what is called the Heisenberg Affair.

In mid-1936, Heisenberg presented his theory of cosmic-ray showers in two papers. Four more papers appeared in the next two years.

In June 1939, Heisenberg bought a summer home for his family in Urfeld, in southern Germany. He also traveled to the United States in June and July, visiting Samuel Abraham Goudsmit, at the University of Michigan in Ann Arbor. However, Heisenberg refused an invitation to emigrate to the United States. He would not see Goudsmit again until six years later, when Goudsmit was the chief scientific advisor to the American Operation Alsos at the close of World War II. Ironically, Heisenberg would be arrested under Operation Alsos and detained in England under Operation Epsilon.

Heisenberg’s paper establishing quantum mechanics has puzzled physicists and historians. His methods assume that the reader is familiar with Kramers-Heisenberg transition probability calculations. The main new idea, noncommuting matrices, is justified only by a rejection of unobservable quantities. It introduces the non-commutative multiplication of matrices by physical reasoning, based on the correspondence principle, despite the fact that Heisenberg was not then familiar with the mathematical theory of matrices. 

In Copenhagen Heisenberg and H. Kramers collaborated on a paper on dispersion, or the scattering from atoms of radiation whose wavelength is larger than the atoms. They showed that the successful formula Kramers had developed earlier could not be based on Bohr orbits, because the transition frequencies are based on level spacings which are not constant. The frequencies which occur in the Fourier transform of sharp classical orbits, by contrast, are equally spaced. But these results could be explained by a semi-classical Virtual State model: the incoming radiation excites the valence, or outer, electron to a virtual state from which it decays. In a subsequent paper Heisenberg showed that this virtual oscillator model could also explain the polarization of fluorescent radiation. These two successes, and the continuing failure of the Bohr-Sommerfeld model to explain the outstanding problem of the anomalous Zeeman effect, led Heisenberg to use the virtual oscillator model to try to calculate spectral frequencies. The method proved too difficult to immediately apply to realistic problems, so Heisenberg turned to a simpler example, the anharmonic oscillator.

The dipole oscillator consists of a simple harmonic oscillator, which is thought of as a charged particle on a spring, perturbed by an external force, like an external charge. The motion of the oscillating charge can be expressed as a Fourier series in the frequency of the oscillator. Heisenberg solved for the quantum behavior by two different methods. First, he treated the system with the virtual oscillator method, calculating the transitions between the levels that would be produced by the external source. He then solved the same problem by treating the anharmonic potential term as a perturbation to the harmonic oscillator and using the perturbation methods that he and Born had developed. Both methods led to the same results for the first and the very complicated second order correction terms. This suggested that behind the very complicated calculations lay a consistent scheme. So Heisenberg set out to formulate these results without any explicit dependence on the virtual oscillator model. To do this, he replaced the Fourier expansions for the spatial coordinates by matrices, matrices which corresponded to the transition coefficients in the virtual oscillator method. He justified this replacement by an appeal to Bohr’s correspondence principle and the Pauli doctrine that quantum mechanics must be limited to observables.

On 9 July, Heisenberg gave Born this paper to review and submit for publication. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices, which he had learned from his study under Jakob Rosanes at Breslau University. Born, with the help of his assistant and former student Pascual Jordan, began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg's paper. A follow-on paper was submitted for publication before the end of the year by all three authors. Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of pure mathematics. Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattices theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics.

Born had learned matrix algebra from Rosanes, as already noted, but Born had also learned Hilbert's theory of integral equations and quadratic forms for an infinite number of variables as was apparent from a citation by Born of Hilbert's work Grundzüge einer allgemeinen Theorie der Linearen Integralgleichungen published in 1912. Jordan, too was well equipped for the task. For a number of years, he had been an assistant to Richard Courant at Göttingen in the preparation of Courant and David Hilbert's book Methoden der mathematischen Physik I, which was published in 1924. This book, fortuitously, contained a great many of the mathematical tools necessary for the continued development of quantum mechanics. In 1926, John von Neumann became assistant to David Hilbert, and he would coin the term Hilbert space to describe the algebra and analysis which were used in the development of quantum mechanics.

In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics, but it was not to be. The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time that it was announced Heisenberg had won the Prize for 1932 "for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen" and Erwin Schrödinger and Paul Adrien Maurice Dirac shared the 1933 Prize "for the discovery of new productive forms of atomic theory". One can rightly ask why Born was not awarded the Prize in 1932 along with Heisenberg – Bernstein gives some speculations on this matter. One of them is related to Jordan joining the Nazi Party on 1 May 1933 and becoming a Storm Trooper. Hence, Jordan's Party affiliations and Jordan's links to Born may have affected Born's chance at the Prize at that time. Bernstein also notes that when Born won the Prize in 1954, Jordan was still alive, and the Prize was awarded for the statistical interpretation of quantum mechanics, attributable alone to Born. Heisenberg's reaction to Born for Heisenberg receiving the Prize for 1932 and to Born for Born receiving the Prize in 1954 are also instructive in evaluating whether Born should have shared the Prize with Heisenberg. On 25 November 1933, Born received a letter from Heisenberg in which he said he had been delayed in writing due to a "bad conscience" that he alone had received the Prize "for work done in Göttingen in collaboration – you, Jordan and I." Heisenberg went on to say that Born and Jordan's contribution to quantum mechanics cannot be changed by "a wrong decision from the outside." In 1954, Heisenberg wrote an article honoring Max Planck for his insight in 1900. In the article, Heisenberg credited Born and Jordan for the final mathematical formulation of matrix mechanics and Heisenberg went on to stress how great their contributions were to quantum mechanics, which were not "adequately acknowledged in the public eye."

On 1 April 1935, the eminent theoretical physicist Arnold Sommerfeld, Heisenberg's doctoral advisor at the University of Munich, achieved emeritus status. However, Sommerfeld stayed in his chair during the selection process for his successor, which took until 1 December 1939. The process was lengthy due to academic and political differences between the Munich Faculty's selection and that of the Reichserziehungsministerium (REM, Reich Education Ministry) and the supporters of Deutsche Physik, which was anti-Semitic and had a bias against theoretical physics, especially quantum mechanics and the theory of relativity. In 1935, the Munich Faculty drew up a list of candidates to replace Sommerfeld as ordinarius professor of theoretical physics and head of the Institute for Theoretical Physics at the University of Munich. There were three names on the list: Werner Heisenberg, who received the Nobel Prize in Physics for 1932, Peter Debye, who would receive the Nobel Prize in Chemistry in 1936, and Richard Becker - all former students of Sommerfeld. The Munich Faculty was firmly behind these candidates, with Heisenberg as their first choice. However, supporters of Deutsche Physik and elements in the REM had their own list of candidates and the battle dragged on for over four years. During this time, Heisenberg came under vicious attack by the Deutsche Physik supporters. One attack was published in Das Schwarze Korps, the newspaper of the Schutzstaffel (SS), headed by Heinrich Himmler. In this, Heisenberg was called a "White Jew" (i.e. an Aryan who acts like a Jew) who should be made to "disappear." These attacks were taken seriously, as Jews were violently attacked and incarcerated. Heisenberg fought back with an editorial and a letter to Himmler, in an attempt to resolve this matter and regain his honour. At one point, Heisenberg's mother visited Himmler's mother. The two women knew each other as Heisenberg's maternal grandfather and Himmler's father were rectors and members of a Bavarian hiking club. Eventually, Himmler settled the Heisenberg affair by sending two letters, one to SS Gruppenführer Reinhard Heydrich and one to Heisenberg, both on 21 July 1938. In the letter to Heydrich, Himmler said Germany could not afford to lose or silence Heisenberg as he would be useful for teaching a generation of scientists. To Heisenberg, Himmler said the letter came on recommendation of his family and he cautioned Heisenberg to make a distinction between professional physics research results and the personal and political attitudes of the involved scientists. The letter to Heisenberg was signed under the closing "Mit freundlichem Gruss und, Heil Hitler!" (With friendly greetings, Heil Hitler!") Overall, the Heisenberg affair was a victory for academic standards and professionalism. However, the appointment of Wilhelm Müller to replace Sommerfeld was a political victory over academic standards. Müller was not a theoretical physicist, had not published in a physics journal, and was not a member of the Deutsche Physikalische Gesellschaft; his appointment was considered a travesty and detrimental to educating theoretical physicists.

During the SS investigation of Heisenberg, the three investigators had training in physics. Heisenberg had participated in the doctoral examination of one of them at the Universität Leipzig. The most influential of the three, however, was Johannes Juilfs. During their investigation, they had become supporters of Heisenberg as well as his position against the ideological policies of the deutsche Physik movement in theoretical physics and academia.

In 1939, shortly after the discovery of nuclear fission, the German nuclear energy project, also known as the Uranverein (Uranium Club), was begun. Heisenberg was one of the principal scientists leading research and development in the project.

From 15 to 22 September 1941, Heisenberg traveled to German occupied Copenhagen to lecture and discuss nuclear research and theoretical physics with Niels Bohr. The meeting, and specifically what it might reveal about Heisenberg's intentions concerning developing nuclear weapons for the Nazi regime, is the subject of the award winning play titled Copenhagen. Documents relating to the Bohr-Heisenberg meeting were released in 2002 by the Niels Bohr Archive and by the Heisenberg family.

On 26 February 1942, Heisenberg presented a lecture to Reich officials on energy acquisition from nuclear fission, after the Army withdrew most of its funding. The Uranium Club was transferred to the Reich Research Council (RFR) in July 1942. On 4 June 1942, Heisenberg was summoned to report to Albert Speer, Germany's Minister of Armaments, on the prospects for converting the Uranium Club's research toward developing nuclear weapons. During the meeting, Heisenberg told Speer that a bomb could not be built before 1945, and would require significant monetary and manpower resources. Five days later, on 9 June 1942, Adolf Hitler issued a decree for the reorganization of the RFR as a separate legal entity under the Reich Ministry for Armament and Ammunition; the decree appointed Reich Marshall Göring as the president.

In September 1942, Heisenberg submitted his first paper of a three-part series on the scattering matrix, or S-matrix, in elementary particle physics. The first two papers were published in 1943 and the third in 1944. The S-matrix described only observables, i.e., the states of incident particles in a collision process, the states of those emerging from the collision, and stable bound states; there would be no reference to the intervening states. This was the same precedent as he followed in 1925 in what turned out to be the foundation of the matrix formulation of quantum mechanics through only the use of observables.

In February 1943, Heisenberg was appointed to the Chair for Theoretical Physics at the Friedrich-Wilhelms-Universität (today, the Humboldt-Universität zu Berlin). In April, his election to the Preußische Akademie der Wissenschaften (Prussian Academy of Sciences) was approved. That same month, he moved his family to their retreat in Urfeld as Allied bombing increased in Berlin. In the summer, he dispatched the first of his staff at the Kaiser-Wilhelm Institut für Physik to Hechingen and its neighboring town of Haigerloch, on the edge of the Black Forest, for the same reasons. From 18–26 October, he traveled to German occupied Netherlands. In December 1943, Heisenberg visited German occupied Poland.

From 24 January to 4 February 1944, Heisenberg traveled to occupied Copenhagen, after the German Army confiscated Bohr's Institute of Theoretical Physics. He made a short return trip in April. In December, Heisenberg lectured in neutral Switzerland.

In January 1945, Heisenberg vacated the Kaiser-Wilhelm Institut für Physik with about all of his staff for the facilities in the Black Forest.

In December 1938, the German chemists Otto Hahn and Fritz Strassmann sent a manuscript to Naturwissenschaften reporting they had detected the element barium after bombarding uranium with neutrons; simultaneously, they communicated these results to Lise Meitner, who had in July of that year fled to the Netherlands and then went to Sweden. Meitner, and her nephew Otto Robert Frisch, correctly interpreted these results as being nuclear fission. Frisch confirmed this experimentally on 13 January 1939.

Paul Harteck was director of the physical chemistry department at the University of Hamburg and an advisor to the Heereswaffenamt (HWA, Army Ordnance Office). On 24 April 1939, along with his teaching assistant Wilhelm Groth, Harteck made contact with the Reichskriegsministerium (RKM, Reich Ministry of War) to alert them to the potential of military applications of nuclear chain reactions. Two days earlier, on 22 April 1939, after hearing a colloquium paper by Wilhelm Hanle on the use of uranium fission in a Uranmaschine (uranium machine, i.e., nuclear reactor), Georg Joos, along with Hanle, notified Wilhelm Dames, at the Reichserziehungsministerium (REM, Reich Ministry of Education), of potential military applications of nuclear energy. The communication was given to Abraham Esau, head of the physics section of the Reichsforschungsrat (RFR, Reich Research Council) at the REM. On 29 April, a group, organized by Esau, met at the REM to discuss the potential of a sustained nuclear chain reaction. The group included the physicists Walther Bothe, Robert Döpel, Hans Geiger, Wolfgang Gentner (probably sent by Walther Bothe), Wilhelm Hanle, Gerhard Hoffmann, and Georg Joos; Peter Debye was invited, but he did not attend. After this, informal work began at the Georg-August University of Göttingen by Joos, Hanle, and their colleague Reinhold Mannfopff; the group of physicists was known informally as the first Uranverein (Uranium Club) and formally as Arbeitsgemeinschaft für Kernphysik. The group's work was discontinued in August 1939, when the three were called to military training.

The second Uranverein began after the Heereswaffenamt (HWA, Army Ordnance Office) squeezed the Reichsforschungsrat (RFR, Reich Research Council) out of the Reichserziehungsministerium (REM, Reich Ministry of Education) and started the formal German nuclear energy project under military auspices. The second Uranverein was formed on 1 September 1939, the day World War II began, and it had its first meeting on 16 September 1939. The meeting was organized by Kurt Diebner, advisor to the HWA, and held in Berlin. The invitees included Walther Bothe, Siegfried Flügge, Hans Geiger, Otto Hahn, Paul Harteck, Gerhard Hoffmann, Josef Mattauch, and Georg Stetter. A second meeting was held soon thereafter and included Klaus Clusius, Robert Döpel, Werner Heisenberg, and Carl Friedrich von Weizsäcker. Also at this time, the Kaiser-Wilhelm Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics, after World War II the Max Planck Institute for Physics), in Berlin-Dahlem, was placed under HWA authority, with Diebner as the administrative director, and the military control of the nuclear research commenced.

When it was apparent that the nuclear energy project would not make a decisive contribution to ending the war effort in the near term, control of the KWIP was returned in January 1942 to its umbrella organization, the Kaiser-Wilhelm Gesellschaft (KWG, Kaiser Wilhelm Society, after World War II the Max-Planck Gesellschaft), and HWA control of the project was relinquished to the RFR in July 1942. The nuclear energy project thereafter maintained its kriegswichtig (important for the war) designation and funding continued from the military. However, the German nuclear power project was then broken down into the following main areas: uranium and heavy water production, uranium isotope separation, and the Uranmaschine (uranium machine, i.e., nuclear reactor). Also, the project was then essentially split up between a number of institutes, where the directors dominated the research and set their own research agendas. The dominant personnel and facilities were the following:

• Institut für Physik (Walther Bothe) of the Kaiser-Wilhelm Institut für medizinische Forschung (KWImF, Kaiser Wilhelm Institute for Medical Research),
• Institute for Physical Chemistry (Klaus Clusius) at the Ludwig Maximilian University of Munich,
• HWA Versuchsstelle (testing station) in Gottow (Kurt Diebner),
• Kaiser-Wilhelm-Institut für Chemie (Otto Hahn),
• Physical Chemistry Department (Paul Harteck) of the University of Hamburg,
• Kaiser-Wilhelm-Institut für Physik (Werner Heisenberg),
• Second Experimental Physics Institute (Hans Kopfermann) at the Georg-August University of Göttingen,
• Auergesellschaft (Nikolaus Riehl), and
• II. Physikalisches Institut (Georg Stetter) at the University of Vienna.

Heisenberg was appointed director-in-residence of the KWIP on 1 July 1942, as Peter Debye was still officially the director and on leave in the United States; Debye had gone on leave as he was a citizen of The Netherlands and had refused to become a German citizen when the HWA took administrative control of the KWIP. Heisenberg still also had his department of physics at the University of Leipzig where work was done for the Uranverein by Robert Döpel and his wife Klara Döpel. During the period Kurt Diebner administered the KWIP under the HWA program, considerable personal and professional animosity developed between Diebner and the Heisenberg inner circle – Heisenberg, Karl Wirtz, and Carl Friedrich von Weizsäcker.

The point in 1942, when the army relinquished its control of the German nuclear energy project, was the zenith of the project relative to the number of personnel devoting time to the effort. There were only about seventy scientists working on the project, with about forty devoting more than half their time to nuclear fission research. After this, the number of scientists working on applied nuclear fission diminished dramatically. Many of the scientists not working with the main institutes stopped working on nuclear fission and devoted their efforts to more pressing war related work.

Over time, the HWA and then the RFR controlled the German nuclear energy project. The most influential people in the project were Kurt Diebner, Abraham Esau, Walther Gerlach, and Erich Schumann. Schumann was one of the most powerful and influential physicists in Germany. Schumann was director of the Physics Department II at the Frederick William University (later, University of Berlin), which was commissioned and funded by the Oberkommando des Heeres (OKW, Army High Command) to conduct physics research projects. He was also head of the research department of the HWA, assistant secretary of the Science Department of the OKW, and Bevollmächtiger (plenipotentiary) for high explosives. Diebner, throughout the life of the nuclear energy project, had more control over nuclear fission research than did Walther Bothe, Klaus Clusius, Otto Hahn, Paul Harteck, or Werner Heisenberg.

Operation Alsos was an Allied effort commanded by the Russian-American Colonel Boris T. Pash. He reported directly to General Leslie Groves, commander of the Manhattan Engineer District, which was developing atomic weapons for the United States. The chief scientific advisor to Operation Alsos was the physicist Samuel Abraham Goudsmit. Goudsmit was selected for this task because of his knowledge of physics, he spoke German, and he personally knew a number of the German scientists working on the German nuclear energy project. He also knew little of the Manhattan Project, so, if he were captured, he would have little intelligence value to the Germans. The objectives of Operation Alsos were to determine if the Germans had an atomic bomb program and to exploit German atomic related facilities, intellectual materials, materiel resources, and scientific personnel for the benefit of the United States. Personnel on this operation generally swept into areas which had just come under control of the Allied military forces, but sometimes they operated in areas still under control by German forces.

Berlin had been a location of many German scientific research facilities. To limit casualties and loss of equipment, many of these facilities were dispersed to other locations in the latter years of the war. The Kaiser-Wilhelm-Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics) had mostly been moved in 1943 and 1944 to Hechingen and its neighboring town of Haigerloch, on the edge of the Black Forest, which eventually became the French occupation zone. This move and a little luck allowed the Americans to take into custody a large number of German scientists associated with nuclear research. The only section of the institute which remained in Berlin was the low-temperature physics section, headed by Ludwig Bewilogua (1906–83), who was in charge of the exponential uranium pile.

Nine of the prominent German scientists who published reports in Kernphysikalische Forschungsberichte as members of the Uranverein were picked up by Operation Alsos and incarcerated in England under Operation Epsilon: Erich Bagge, Kurt Diebner, Walther Gerlach, Otto Hahn, Paul Harteck, Werner Heisenberg, Horst Korsching, Carl Friedrich von Weizsäcker, and Karl Wirtz. Also, incarcerated was Max von Laue, although he had nothing to do with the nuclear energy project. Goudsmit, the chief scientific advisor to Operation Alsos, thought von Laue might be beneficial to the postwar rebuilding of Germany and would benefit from the high level contacts he would have in England. Heisenberg had been captured and arrested by Colonel Pash at Heisenberg's retreat in Urfeld, on 3 May 1945, in what was a true alpine-type operation in territory still under control by German forces. He was taken to Heidelberg, where, on 5 May, he met Goudsmit for the first time since the Ann Arbor visit in 1939. Germany surrendered just two days later. Heisenberg would not see his family again for eight months. Heisenberg was moved across France and Belgium and flown to England on 3 July 1945.

The ten German scientists were held at Farm Hall in England. The facility had been a safe house of the British foreign intelligence MI6. During their detention, their conversations were recorded. Conversation thought to be of intelligence value were transcribed and translated into English. The transcripts were released in 1992. Bernstein has published an annotated version of the transcripts in his book Hitler's Uranium Club: The Secret Recordings at Farm Hall, along with an introduction to put them in perspective. A complete, unedited publication of the British version of the reports appeared as Operation Epsilon: The Farm Hall Transcripts, which was published in 1993 by the Institute of Physics in Bristol and by the University of California Press in the United States.

On 3 January 1946, the ten Operation Epsilon detainees were transported to Alswede, Germany, which was in the British occupation zone. Heisenberg settled in Göttingen, also in the British zone. In July, he was named director of the Kaiser-Wilhelm Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics), then located in Göttingen. Shortly thereafter, it was renamed the Max-Planck Institut für Physik, in honor of Max Planck and to assuage political objections to the continuation of the institute. Heisenberg was its director until 1958. In 1958, the institute was moved to Munich, expanded, and renamed Max-Planck-Institut für Physik und Astrophysik (MPIFA). Heisenberg was its director from 1960 to 1970; in the interim, Heisenberg and the astrophysicist Ludwig Biermann were co-directors. Heisenberg resigned his directorship of the MPIFA on 31 December 1970. Upon the move to Munich, Heisenberg also became an ordentlicher Professor (ordinarius professor) at the University of Munich.

Just as the Americans did with Operation Alsos, the Russians inserted special search teams into Germany and Austria in the wake of their troops. Their objective, under the Russian Alsos, was also the exploitation of German atomic related facilities, intellectual materials, materiel resources, and scientific personnel for the benefit of the Soviet Union. One of the German scientists recruited under this Russian operation was the nuclear physicist Heinz Pose, who was made head of Laboratory V in Obninsk. When he returned to Germany on a recruiting trip for his laboratory, Pose wrote a letter to the Werner Heisenberg inviting him to work in Russia. The letter lauded the working conditions in Russia and the available resources, as well as the favorable attitude of the Russians towards German scientists. A courier hand delivered the recruitment letter, dated 18 July 1946, to Heisenberg; Heisenberg politely declined in a return letter to Pose.

In 1947, Heisenberg presented lectures in Cambridge, Edinburgh, and Bristol. Heisenberg also contributed to the understanding of the phenomenon of superconductivity with a paper in 1947 and two papers in 1948, one of them with Max von Laue. In the period shortly after World War II, Heisenberg briefly returned to the subject of his doctoral thesis, turbulence. Three papers were published in 1948 and one in 1950. In the post-war period, Heisenberg continued his interests in cosmic-ray showers with considerations on multiple production of mesons. He published three papers in 1949, two in 1952, and one in 1955.

On 9 March 1949, the Deutsche Forschungsrat (German Research Council) was established by the Max-Planck Gesellschaft (MPG, Max Planck Society, successor organization to the Kaiser-Wilhelm Gesellschaft. Heisenberg was appointed president of the Deutsche Forschungsrat. In 1951, the organization was fused with the Notgemeinschaft der Deutschen Wissenschaft (NG, Emergency Association of German Science) and that same year renamed the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). With the merger, Heisenberg was appointed to the presidium. In 1952, Heisenberg served as the chairman of the Commission for Atomic Physics of the DFG. Also that year, he headed the German delegation to the European Council for Nuclear Research. In 1953, Heisenberg was appointed president of the Alexander von Humboldt-Stiftung by Konrad Adenauer. Heisenberg served until 1975. Also, from 1953, Heisenberg's theoretical work concentrated on the unified field theory of elementary particles.

In late 1955 to early 1956, Heisenberg gave the Gifford Lectures at St Andrews University, in Scotland, on the intellectual history of physics. The lectures were later published as Physics and Philosophy: The Revolution in Modern Science.

During 1956 and 1957, Heisenberg was the chairman of the Arbeitskreis Kernphysik (Nuclear Physics Working Group) of the Fachkommission II "Forschung und Nachwuchs" (Commission II "Research and Growth") of the Deutschen Atomkommission (DAtK, German Atomic Energy Commission). Other members of the Nuclear Physics Working Group in both 1956 and 1957 were: Walther Bothe, Hans Kopfermann (vice-chairman), Fritz Bopp, Wolfgang Gentner, Otto Haxel, Willibald Jentschke, Heinz Maier-Liebnitz, Josef Mattauch, Wolfgang Riezler, Wilhelm Walcher, and Carl Friedrich von Weizsäcker. Wolfgang Paul was also a member of the group during 1957.

In 1957, Heisenberg was a signatory of the manifesto of the Göttinger Achtzehn (Göttingen Eighteen).

From 1957, Heisenberg was interested in plasma physics and the process of nuclear fusion. He also collaborated with the International Institute of Atomic Physics in Geneva. He was a member of the Institute's Scientific Policy Committee, and for several years was the Committee's chairman.

In 1973, Heisenberg gave a lecture at Harvard University on the historical development of the concepts of quantum theory.

On 24 March 1973, Heisenberg gave a speech before the Catholic Academy of Bavaria, accepting the Romano Guardini Prize. An English translation of its title is "Scientific and Religious Truth." And its stated goal was "In what follows, then, we shall first of all deal with the unassailability and value of scientific truth, and then with the much wider field of religion, of which -- so far as the Christian religion is concerned -- Guardini himself has so persuasively written; finally -- and this will be the hardest part to formulate -- we shall speak of the relationship of the two truths."

In January 1937 Heisenberg met Elisabeth Schumacher at a private music recital. Elisabeth was the daughter of a well-known Berlin economics professor. They were married on 29 April. The fraternal twins, Maria and Wolfgang, were born to them in January 1938, whereupon, Wolfgang Pauli congratulated Heisenberg on his "pair creation" – a word play on a process from elementary particle physics, pair production. They had five more children over the next 12 years: Barbara, Christine, Jochen, Martin, and Verena. Jochen became a physics professor at the University of New Hampshire.

Heisenberg enjoyed classical music and was an accomplished pianist.

Heisenberg died of cancer of the kidneys and gall bladder at his home, on 1 February 1976. The next evening, his colleagues and friends walked in remembrance from the Institute of Physics to his home and each put a candle near the front door.