## The Homecoming of the Expelled Son

Who founded quantum mechanics? Erwin Schrödinger (1887-1961) and Werner Heisenberg (1901-1976) come to mind first, one with the wave equation named after him, the other with the uncertainty principle, both 1932 and 1933 with Nobel prizes Much less known is the role of Heisenberg's teacher Max Born (1882-1970). Born not only introduced the term quantum mechanics in 1926, but also provided the mathematical basis for the so-called Heisenberg picture of quantum physics. With this formalism, the physics is in time-dependent observables, that is, in observable quantities such as position and momentum. Heisenberg now discovered that these quantities in quantum physics can be described by non-commutative quantities.

Ordinary numbers are commutative, which means that when you multiply them, the order doesn't matter. What unusual mathematical objects are these non-commutative quantities? Max Born, the mathematician among the quantum physicists, gave the answer: They are matrices. With such two-dimensional arrays of numbers in rows and columns, it really makes a difference how you multiply them. Born expressed this in July 1925 with the matrix formula pq-qp=(h/2πi)I, which is on his gravestone in Göttingen today; where p denotes momentum, q the position, h Planck's constant and I the identity matrix. Heisenberg's famous uncertainty relation is a consequence of this formula. The "three-man work" by Max Born, Werner Heisenberg and PascualJordan, published in the "Zeitschrift fürPhysik" in 1926, established matrix mechanics, which was later identified only with Heisenberg.

An alternative – and as it soon turned out, equivalent – formulation of quantum mechanics is the Schrödinger picture. The physics are in the time-dependent Schrödinger wave function Ψ. Born also made a significant contribution to this formalism by interpreting the wave function as a "probability wave": The value of this function indicates the probability with which a state measurement has a certain result. With this, Born specified the statistical character of quantum mechanics. The state function Ψ obeys the deterministic Schrödinger equation, but the state itself is not clearly defined, but includes the entirety of all more or less probable measurement results.

Born - for his mathematician colleague Norbert Wiener "the most humble scholar I know" - suffered all his life from the fact that his contribution to quantum physics was underestimated, and felt the award of the Nobel Prize in 1954 as belated satisfaction it took a long time before a representative biography was dedicated to this "master builder of the quantum world". The American author Nancy Greenspan follows almost daily the fate of the quiet scholar and stimulating teacher whose classes have produced nine Nobel Prize winners. Like all quantum physicists, Born was confronted, albeit indirectly, with the problem of the atomic bomb. In Göttingen, one of his students in 1926/27 was Robert Oppenheimer, later head of the Manhattan Project and "father of the bomb". At the time, Born had trouble putting up with Oppenheimer's child prodigy airs, but gave his dissertation top marks and developed the "Born-Oppenheimer approximation" for the Schrödinger equation of molecules with him. Later, in 1938, the "nuclear spy" Klaus Fuchs also received his doctorate from Born. Fuchs then worked on the British and American bomb programs; because he saw a threat to world peace in the West's nuclear monopoly, he provided the Soviet Union with secret data on the physics of the atomic bomb.

Born came from the German educated middle class; the fact that he was of Jewish origin only played a role for him when the Nazis covered the universities with their racist terror. Born had to emigrate and finally found an academic home in Edinburgh. Relatives and friends were killed in German concentration camps. That's why Albert Einstein, with whom Born had a lifelong friendship, couldn't understand that Born nevertheless returned to Germany after the war, "to the land of the mass murderers", as Einstein wrote to him.

Born's relationship with Heisenberg was also tricky at times, about whom he judged in a private letter at the end of 1947: "His philosophy of life is undoubtedly somewhat infected by Nazi thoughts … Apparently he regrets more that the Germans didn't turn out to be the strongest than what we felt for the sad and regrettable things."

Despite everything, Born returned home to "help work for a spiritual renewal of Germany". In his late years he was a leading member of the "Göttinger Eighteen" - including Heisenberg - against nuclear armament in the Federal Republic and for general disarmament. Schools and streets in his homeland are named after him today. The German edition of this biography completes the homecoming of the expelled son.