In developing quantum mechanics of pointlike particles one is faced with a curious, almost paradoxical situation: One seeks a more general theory which takes proper account of Planck’s quantum of action h and which encompasses classical mechanics, in the limit h ? 0, but for which initially one has no more than the formal framework of canonical mechanics. This is to say, slightly exaggerating, that one tries to guess a theory for the hydrogen atom and for scattering of electrons by extrapolation from the laws of celestial mechanics.That this adventure eventually is successful rests on both phenomenological and on theoretical grounds. On the phenomenological side we know that there are many experimental findings which cannot be interpreted classically and which in some cases strongly contradict the predictions of classical physics. At the same time this phenomenology provides hints at fundamental properties of radiation and of matter which are mostly irrelevant in macroscopic physics: Besides its classically well-known wave nature light also possesses particle properties; in turn massive particles such as the electron have both mechanical and optical properties.This discovery leads to one of the basic postulates of quantum theory, de Broglie’s relation between the wave length of a monochromatic wave and the momentum of a massive or massless particle in uniform rectilinear motion.