Early Days of Quantum Theory

H. J. Carmichael

​In this year of light, our attention is quickly drawn to the many inroads into our day-to-day lives made, since the early 1960s, by the laser and the various technologies it has spawned: digital technologies (e.g. the optical fibre network), biomedical imaging and applications (e.g. in ophthalmology and dermatology), and applications in precision and ‘not-so-precision’ engineering – how did engineers ensure that the ends of the Chunnel would meet up in the middle? Likely only a very few of us are turned to a reflection on quantum mechanics by the year of light; but the rise of light, from its rather side-lined position in the late nineteenth century, as a well-understood Maxwell wave, to its position today as a diverse enabling technology, is very much a story of quantum mechanics, particularly in its early days, the days of the Old Quantum Theory where my tale of quantum jumps begins.

Detlef Dürr, Stefan Teufel

Jagdish Mehra, Helmut Rechenberg

S. Rajasekar, R. Velusamy

The WKB approximation is a physically intuitive method and makes many connections with intuition about waves and classical mechanics as well as with results from the early days of quantum theory as it leads to the Bohr quantization condition. The WKB method is due to Gregor Wentzel, Hendrik Anthony Kramers and Leon Nicolas Brillouin. The method is applicable for slowly varying potentials, that is, the potentials that change not more than a few wavelengths. The WKB approximation is a physically intuitive method and makes many connections with intuition about waves and classical mechanics as well as with results from the early days of quantum theory as it leads to the Bohr quantization condition. The Schrödinger equation is solved to find the penetration of a square potential barrier. The WKB method is applied to obtain a transmission coefficient for penetration through a barrier.

Amnon Yariv

A description by the author of the early days of nonlinear optics (NLO), and the motivation for the formulation of the quantum theory of NLO, implications to a number of diverse areas, and the background for the prediction of spontaneous parametric fluorescence.

Hendrik B. G. Casimir