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.

The existence of a Cosmic Microwave Background was theoretically predicted by George Gamow and his associates, but played no role in the accidental discovery of the 2.7 degree cosmic microwave background radiation by Penzias and Wilson while they were testing a new type of satellite communications antenna at the Bell Telephone Laboratories in Holmdel, NJ. An earlier measurement of the cosmic microwave background at Bell Labs went unnoticed except by Russian scientists, who misunderstood the paper to be reporting a negative result. Meanwhile, not far away, Robert Dicke and his colleagues at Princeton University were building a radiometer to verify Dicke’s prediction that it might be possible to detect the microwave remnants of the big-bang. But they were beaten by Penzias and Wilson’s serendipitous Nobel Prize winning discovery that led to the final demise of the steady-state theory. An even earlier measurement of optical absorption lines by interstellar cyanogen gave the first clues to the existence of a cosmic background radiation, but its meaning was not recognized until after the 1965 experimental discovery of the microwave background at Bell Labs.

Max Planck was an expert on classical thermodynamics and turned his attention to the understanding of black-body radiation in 1895. He worked out the form the radiation formula had to have from the emission and absorption of radiation of a dipole in thermal equilibrium with the radiation it emits. The formula related the mean energy density of radiation to the average energy of the oscillator. Using new precision measurements of the black-body spectrum, Planck derived the primitive form of the black-body spectrum by a combination of theory and the empirical results of experiment, but without any physical interpretation of the significance of the formula.