Ehrenfest’s adiabatic hypothesis and the old quantum theory, 1916–1918

Enric Pérez Canals

Daniel M. Greenberger, Klaus Hentschel, Friedel Weinert

Pérez, Enric, Blai Pié Valls

It is widely known that Paul Ehrenfest formulated and applied his adiabatic hypothesis in the early 1910s. Niels Bohr, in his first attempt to construct a quantum theory in 1916, used it for fundamental purposes in a paper which eventually did not reach the press. He decided not to publish it after having received the new results by Sommerfeld in Munich. Two years later, Bohr published "On the quantum theory of line-spectra." There, the adiabatic hypothesis played an important role, although it appeared with another name: the principle of mechanical transformability. In the subsequent variations of his theory, Bohr never suppressed this principle completely. We discuss the role of Ehrenfest's principle in the works of Bohr, paying special attention to its relation to the correspondence principle. We will also consider how Ehrenfest faced Bohr's uses of his more celebrated contribution to quantum theory, as well as his own participation in the spreading of Bohr's ideas.

Marco Giliberti, Luisa Lovisetti

L.D. Faddeev, L.A. Khalfin, I.V. Komarov

In old quantum mechanics the adiabatic theorem established by Ehrenfest had the meaning that the quantized action variables J = n are invariant relative to an infinitely slow (adiabatic) change of a mechanical system.1 From this one can guess that if the system is in a state with definite quantum numbers before the adiabatic change started, then after the changes it will be characterized by the same quantum numbers.