The topic of this chapter is the wave function – what it is, how it is to be interpreted and how information can be extracted from it. To this end, the notion of operators in quantum physics is introduced. And the statistical interpretation called the Born interpretation is discussed. This discussion also involves terms such as expectation values and standard deviations. The first part, however, is dedicated to a brief outline of how quantum theory came about – who were the key people involved, and how the theory grew out of a need for understanding certain natural phenomena. Parallels are drawn to the historical development of our understanding of light. At a time when it was generally understood that light is to be explained in terms of travelling waves, an additional understanding of light consisting of small quanta turned out to be required. It was in this context that Louis de Broglie introduced the idea that matter, which finally was known to consist of particles – atoms – must be perceived as waves as well. Finally, formal aspects such as Dirac notation and inner products are briefly addressed. And units are introduced which allow for convenient implementations in the following chapters.

This chapter provides a brief overview of the history of the development of quantum theory, with a critical focus on the antirealist tradition inaugurated by Niels Bohr. The distinction between “principle theories” and “constructive theories” is discussed, and it is noted that quantum mechanics is a “principle theory.” It is argued that quantum theory is amenable to a fully realist interpretation provided we let go of the demand that reality be classically picturable.

This chapter covers the early years of quantum theory, a time of guesswork, inspired by problems presented by the properties of atoms and radiation and their interaction. Later, in the 1920s, this struggle led to the systematic theory known as quantum mechanics, the subject of Chapter 5. Quantum mechanics started with the problem of understanding radiation in thermal equilibrium at a non-zero temperature. It was not possible to make progress in applying quantum ideas to atoms without some understanding of what atoms are. The growth of this understanding began with the discovery of radioactivity.