Practising the correspondence principle in the old quantum theory : Franck, Hund and the Ramsauer effect

Martin Jähnert

Martin Jähnert

Anthony Duncan A, Michel Janssen B

The explanation of the first-order Stark effect in hydrogen by Epstein and Schwarzschild in 1916 was seen as a great success for the old quantum theory. Yet, it also revealed some serious limitations of the theory. To recover the experimentally found line splittings, one had to make some arbitrary assumptions in addition to the basic quantum conditions to rule out certain orbits. The calculation of intensities of lines on the basis of Bohr's correspondence principle likewise required arbitrary additional assumptions. Finally, the actual orbits predicted by the old quantum theory depend on the coordinates chosen to impose the quantum conditions. Both Sommerfeld and Epstein recognized this problem but offered no solution for it. All these problems were solved in 1926 when Schrödinger and Epstein explained the Stark effect on the basis of the new wave mechanics. The calculations in the two theories are similar. In particular, both the Schrödinger equation in the new theory and the Hamilton-Jacobi equation in the old theory are separated in parabolic coordinates. The new quantum mechanics determines all allowed states and transitions without any additional assumptions. It also replaced the ambiguous guidelines based on the correspondence principle for calculating intensities by the straightforward prescription that intensities are given by the squares of the matrix elements of position, leading to results that agreed much better with the experimental data. Finally, the embarrassing non-uniqueness of orbits in the old quantum theory turned into the innocuous non-uniqueness of bases of eigenfunctions in wave mechanics. To this day, the Stark effect is remembered as one of the few qualified successes of the old quantum theory. We suspect that this is largely because after 1926 it became just one of the many unqualified successes of the new quantum theory.

Yalçin Koç

Insok Ko

Blai Pié Valls, Enric Pérez Canals

It is widely known that both the Correspondence Principle and the Adiabatic Principle were the two pillars of Bohr's quantum theory. However, the Correspondence Principle usually gets much more attention in historical accounts. A closer look at Bohr's quantum theory shows that, although the fate of the Adiabatic Principle was closely tied up with the validity of mechanics, it also played a significant role in the old quantum theory. In the early 1920s, when dealing with multielectron atoms, Bohr was forced to reshape the theory and thus to reconsider the relative relevance of the two principles. It is precisely the late preponderance of the Correspondence Principle which has, in perspective, biased the historical weight attributed to each of them.