Bohr’s molecular model and the melding of classical and quantum mechanics

Permit me to add some information to the article entitled, “Bohr’s molecular model, a century later.” The authors discuss the idea of “dimensional scaling,” approximating the spectra of atoms and molecules by employing perturbation theory to expand around the infinite-dimension/classical limit. That technique of approximating the Schrödinger equation, originally called the 1/N expansion, was developed and applied to numerous problems in the 1980s, including simple atoms, quarkonium, and the hydrogen molecule. ^{1 , 2 , 3} It grew out of attempts in the 1970s to formulate quantum chromodynamics in the limit of a large number of colors. The use of the 1/N expansion in atomic physics was discussed by Edward Witten (Physics Today, July 1980, page 38 ), who pointed out that his discussion was based on work that applied the method to hydrogen and helium atoms. ¹

The work in reference made use of algebraic methods for the analysis, but the coordinate space method was also developed and was initially used to treat the strong-field Zeeman effect. ² A nice description of the status of the field at the time was given by Laurence Yaffe (Physics Today, August 1983, page 50 ). Many additional applications of that method in the physics literature may be found in reference .