Quantum Theory: General Principles

Abstract

In this chapter, which is central to this book, the general principles of quantum theory will be discussed, in its simplest form, i.e. excluding at this point statistical quantum theory, to be discussed in Chap. 11. We start in 3.2 and 3.3 with the historical context, sketching the problems in classical physics at the end of the nineteenth century, the first attempt of a solution by an ingenious intuitive idea of Niels Bohr in the early twentieth century, and finally, the creation of a fully fledged new theory which took care of the problems. A very successful physical theory, however not very well understood mathematically; neither in some of its details nor in its general structure. It was John von Neumann, stimulated by David Hilbert, two of the greatest mathematicians of the twentieth century, who in the 1920s developed a clear and rigorous framework for quantum theory, in terms of new mathematics, functional analysis, and in particular the theory of operators in Hilbert space, which is by now the generally accepted mathematical basis of quantum theory. For this reason this chapter should be read with Supp. Chap. 21 at hand, in particular by a reader who is not familiar with this material