The present collection of papers is devoted to a rather new and very controversial topic, the so-called “quantum chaos”. Some researchers see nothing essentially new at all in this phenomenon (apart from a number of various examples and models), and they have good reason to believe so. Indeed, the problems in this field all belong to the traditional, “old-fashion”, and rather “simple” quantum mechanics of finite-dimensional systems with a given interaction and no quantized fields. Nevertheless, many, including ourselves, consider quantum chaos to be a new discovery, though in an old field, of a great importance for fundamental physics. To understand this, the phenomenon of quantum chaos should be put into its proper perspective in recent developments in physics. The central point of this perspective is the conception of dynamical chaos (also a rather new topic) in classical mechanics (for a good review see, e.g., Refs.[l-3]). Thus before discussing the current understanding of quantum chaos we need briefly to describe classical dynamical chaos
Abstract We provide an overview, as non‐technical as possible, of the contents of Vol. 1 of the book. Reflecting the structure of the volume, this overview consists of two parts. In the first part, we summarize the most important early contributions to quantum theory (covered in detail in Chs. 2–4). This part starts with Planck’s work on black‐body radiation culminating in the introduction of Planck’s constant in 1900. It then moves on to Einstein’s 1905 light‐quantum hypothesis, his theory of specific heats, and his formulas for energy and momentum fluctuations in black‐body radiation. After summarizing Bohr’s path to his quantum model of the atom, it concludes with Einstein’s 1916–17 radiation theory combining elements of Bohr’s model with his own light‐quantum hypothesis. In the second part we summarize our analysis of the old quantum theory (given in detail in Chs. 5–7). After a brief overview of the career of Sommerfeld, who together with Bohr took the lead in developing the old quantum theory, we review the three principles we have identified as the cornerstones of the theory (the quantization conditions, the adiabatic principle, and the correspondence principle). We then discuss three of the theory’s most notable successes (fine structure, Stark effect, X‐ray spectra) and, finally, three of its most notorious failures (multiplets, Zeeman effect, helium).