Werner Heisenberg (1901-1976).

Autograph letter signed (‘Werner Heisenberg’) to [Paul Epstein: ‘Sehr geehrter Herr Kollege!’], Ann Arbor, 22 July [1939].

In German. Three pages, 276 x 180mm (marginal tears and short closed tear grazing one word on f.2). Provenance: by descent from the recipient.

Heisenberg on ferromagnetism and quantum spin: weighing up the latest work of his one-time doctoral student, Felix Bloch. Heisenberg thanks Epstein for two previous letters on ferromagnetism (‘Sättigungsmagnetisierung’), before turning immediately to the usefulness of ‘Bloch’s calculation’ (‘Blochsche Rechnung’): ‘On the question of how good Bloch’s calculation is I have still not come to full clarity. I still do not completely understand why the periodicity condition for the open unend[ing] chain gives something different from the closed one’. He goes on to describe the ferromagnetic state in a one-dimensional model – a chain of quantum spins or quantum magnetic moments – in reference to Bloch’s formula: ‘The lowest energy value belongs to the term in which all spins stand parallel s = ½N. This total spin s = ½N may nevertheless adjust in all directions, it can also first be m = s = ½N, i.e. r = 0, or it can be, for example, m = s – 1 = ½N – 1, and r = 1 etc., i.e. physically, this lowest energy value will happen once to every r when it is acting outside the field’. Heisenberg ends his letter undecided over the conditions under which Bloch’s formula applies: ‘For the linear and for the grid surface, Bloch’s calculation is not allowed, but for the three-dimensional it is probably in order’.

In June 1939, immediately before the outbreak of World War II, Heisenberg travelled to the United States to lecture and visit colleagues at the University of Michigan; while residing in Ann Arbor, he corresponded with many of his fellow scientists, including Paul Epstein. The present letter seems to refer to research published in 1936 by Felix Bloch (1905-1983) on calculating the magnetic moment of free neutrons. Bloch had been Heisenberg’s first doctoral student at the University of Leipzig in the late 1920s, when he made important contributions to the quantum mechanics of electrons in crystals and developed the theory of metallic conduction; by 1939 he was working at Stanford University, collaborating with L.W. Alvarez at the Berkeley Cyclotron to calculate the magnetic moment of the neutron.

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