1900–1962: From Planck to Bohr

Léon Brillouin

Olivier Darrigol, Bertrand Duplantier, J. M. Raimond +1 more

Ghazi Q. Hassoun, Donald H. Kobe

Planck formulated the correspondence principle between quantum and classical mechanics as the limit in which the Planck constant h goes to zero. Bohr formulated the correspondence principle to be the limit of large quantum numbers. For three common quantum mechanical systems it is shown that in order for eigenvalues of quantum mechanical observables to have meaningful classical limits, it is necessary to take the double limit as both the Planck constant goes to zero and the quantum number goes to infinity, subject to the constraint that their product is equal to an appropriate classical action. This synthesis of the Bohr and Planck formulations of the correspondence principle is also used to show that the quantum mechanical transition frequency between adjacent levels approaches the corresponding classical frequency. The features these systems have in common in their classical limit are explained by general considerations of the classical limit of the Schrödinger equation.

Jorge Henrique de Oliveira Sales, Suzuki, A. T., D. S. Bonafe

We present in this work a pedagogical way of quantizing the atomic orbit for the hydrogen's atom model proposed by Bohr without using his hypothesis of angular momentum quantization. In contrast to the usual treatment for the orbital quantization, we show that using energy conservation, correspondence principle and Plank's energy quantization Bohr's hypothesis can be deduced from and is a consequence of the Planck's energy quantization.

Bruce W. Shore

Chapter 3 reviews the traditional historical, schoolbook notions of thermal radiation quanta found in the work of Planck, the traveling and absorbed quanta of Einstein, the spectroscopic evidence associated with the atom transitions of Bohr, and the scattering evidence of Compton – experiments that resulted in seemingly conicting views of photons as particles and as waves. It comments on revisionist views that have made these four experimental works no longer the definitive evidences for photons that they once were regarded.

André Avramesco