The first quarter of the twentieth century saw two great scientific revolutions: firstly relativity, which deeply changed our view of space and time, and secondly quantum mechanics, which deeply changed the way we think about states of matter and energy. Quantum mechanics provided a deep understanding of a wide variety of phenomena, from the most fundamental properties of elementary particles to many aspects of chemistry. Quantum theory opened the door to the micro-cosmos, thereby explaining many of the properties of vastly different types of materials such as insulators, metals, semiconductors and superconductors. Modern physics is still deeply involved in further exploiting the ever-surprising worlds of quantum solids, liquids and gases.

The quantum revolution implied a radical shake-up of the foundations of theoretical physics. It was caused among others by the inadequacy of the classical theories of Newton and Maxwell to account for the observed structure of atoms. The atom supposedly consisted of a positively charged nucleus surrounded by a number of negatively charged electrons, exactly compensating the nuclear charge. The problem that arose may be explained as follows. Newton told us that in the proposed configuration the electrons would ‘circle’ very rapidly around the nucleus (like a tiny planetary system), and therefore these electrons would continuously be strongly accelerated. Maxwell, however, told us that an accelerated charge would start radiating and thereby losing energy at an appreciable rate, so that in the end the electrons would fall into the nucleus. A little calculation showed that the lifetime of the atom would be something like a billionth of a second. According to our theoretical knowledge, therefore, atoms would just not exist, bluntly contradicting the observations.

Quantum theory came to the rescue. Looking back, one of the outstanding achievements of quantum theory is that it explained the structure but also the stability of atoms and molecules, and therefore of all matter. In quantum theory the atomic bound states of the electrons with the nucleus form a discrete set – the allowed states are quantized, with a stable lowest energy state.

The theory is based on a number of postulates which are of great generality, providing a framework that should in principle be applicable to any physical system. To put it briefly: our world is quantum-mechanical.