Max-Born-Institut Berlin (MBI)

i(pq - qp) = (h/2π),
statistical
of
48
Max Born • Paul Corkum
In 1921, Max Born was appointed to a chair in Göttingen as the successor to Peter Debye.
Together with James Franck, whose appointment to a post at Göttingen he made a precondition
for accepting his own chair, and Robert Wichard Pohl, Born then became the founder of
the famous Göttingen School. At this time Born began to concern himself with the quantum
physics of atoms. Basic inadequacies had become apparent in Bohr’s treatment of the atom
model. The conformity of quantum physics at the time with classical physics, maintained via
the correspondence principle, had led to quantum rules that could be used to describe the simple
hydrogen atom, but which already failed in their treatment of problems of even slightly
greater complexity, such as the scattering of light and the influence of static magnetic and electric
fields.
The interest of Max Born and his colleagues in atomic physics was attracted by the lectures
given by Niels Bohr in Göttingen in 1922. Initially, they sought a solution in Göttingen within
the framework of many-body models oriented to classical physics. Born’s assistant, Werner Heisenberg,
then succeeded in finding the solution during his famous trip to Heligoland in 1925.
Heisenberg treated the spectral lines of the atom on the basis of a system of oscillators by
replacing the classical amplitudes of the emitted radiation by quantum-theory amplitudes,
which depend on two figures characterizing the transition from one state to another. He succeeded
in transcribing Bohr’s quantum condition within the framework of the same assumptions
and discovered that his formulation perfectly fulfilled the principle of the conservation of
energy, which had been a problem for earlier treatments of semi-classical concepts.
Fulfilling Ritz’s combination principle required the rule of noncommutative multiplication. After
Heisenberg’s return from Heligoland, Born recognized that the result intuitively discovered by
Heisenberg was the formation of a product of matrices. Today we know Max Born’s formulation,
i(pq - qp) = (h/2π), which is also inscribed on his gravestone in Göttingen, in the form of
Heisenberg’s commutation relations between the components of the operator of the space
coordinate and the component of momentum. Born thus became the father of the matrix formulation
of quantum theory.
In the following years, Born devoted himself to the application of quantum mechanics to
nonperiodic and time-dependent processes, especially of scattering theory. In 1933 he wrote
his famous book on optics, which, when forced into exile in Edinburgh by the Nazis, he
later revised with Emil Wolf and republished in 1959 as “The Principles of Optics”. This book,
which we still use as a reference in my institute even today, has since become a standard
work of modern optics.