Getting closer to the Bohr model

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.

OpenStaxCollege

Paul A. Flowers, Edward J. Neth, William R. Robinson +2 more

Werner A. Hofer

I revisit the reply of Bohr to Einstein. Bohr's assertion that there are no causes in atomic scale systems is, as a closer analysis reveals, not in line with the Copenhagen interpretation since it would contain a statement about reality. What Bohr should have written is that there are no causes in mathematics, which is universally acknowledged. The law of causality requires physical effects to be due to physical causes. For this reason any theoretical model which replaces physical causes by mathematical objects is creationism, that is, it creates physical objects out of mathematical elements. I show that this is the case for most of quantum mechanics.

A S Dickinson, Florent Xavier Gadéa, Thierry Leininger

Upper and lower bounds are estimated for the scattering length, a , for the various isotopes of spin-polarized metastable helium. From a previous study involving various large basis sets and two ab initio approaches, and paying special attention to combine them with the accurate long-range potential, we get, for 4 He*– 4 He* collisions (in Bohr) 152 < 4−4 a < 230 and for 3 He*– 3 He* collisions 94 < 3−3 a < 113, while a surprising result arises for mixed collisions, 3 He*– 4 He*, 3−4 a < −488 and 3−4 a > 865. Indeed, the scattering length for this species is very close to the divergence occurring at the binding of a 14th vibrational level. Within these limits, our approach suggests that the values for 4−4 a and 3−3 a are closer to their upper bounds than to their lower bounds, and that the value for 3−4 a is negative and very large (>500) in magnitude. Sympathetic cooling could therefore be very efficient for the mixed species. Cooling-rate coefficients are also evaluated: they are large, of order 10 −9 cm 3 s −1 at mK temperatures for all combinations.