Quantum Statistics

Already in the second half of the nineteenth century, physicists had realized that, for understanding the structure of matter, it was particularly important to be able to address situations where the considered particles were numerous. Therefore, the need to be able to handle systems called “with many bodies” emerged, and consequently, the 1920s and 1930s witnessed the development of new statistics. In this chapter, after a brief introduction to the early studies on cosmic rays, we will present the classical Maxwell–Boltzmann statistics and the quantum statistics of Bose–Einstein and Fermi–Dirac. We will then discuss the relationship between these three different statistics, considering their most important features and some of their applications to explain the structure of matter around us and beyond.