Old Quantum Theory and Early Quantum Mechanics

Biao Wu

Ian Colin Percival

For many physicists who live on intimate terms with atoms, molecules, solids or particles, classical mechanics is a necessary evil, sometimes needed to provide a Hamiltonian or Lagrangian, and hastily abandoned when it has served this purpose. It was not always so: those who worked with Niels Bohr and Max Born in the early 1920s had no quantum mechanics to turn to: they had to do their best with classical mechanics and the old quantum theory.

Luisa Lovisetti, Marco Giliberti

Anthony Duncan A, Michel Janssen B

Abstract This chapter covers the history of dispersion theory starting from the classical theories of the late nineteenth century, involving charged harmonic oscillators with resonance frequencies at the absorption frequencies of the dispersing materials to account for anomalous dispersion, the phenomenon that the index of refraction decreases rather than increases with frequency around the absorption frequencies. It then covers dispersion theories formulated in the context of the old quantum theory, in which the link between radiation frequencies and orbital frequencies is severed. Drawing on these efforts, especially by Ladenburg and Reiche in the early 1920s, and using Bohr’s correspondence principle and other ingredients of the old quantum theory, Kramers found a successful quantum formula in late 1923. He only published a full treatment of his new dispersion theory in a paper with Heisenberg in early 1925. This paper played a key role in laying the foundations of matrix mechanics.