The exchange of particles in the system of two identical particles (which is mathematically equivalent to the rotation of each particle by 180 degrees) results either in the change of the sign of wave function of the system (when the particles have half-integer spin) or not (when the particles have integer spin). The Pauli exclusion principle follows mathematically from the definition of the angular momentum operator ( rotation operator) in quantum mechanics. The Pauli exclusion principle underpins many of the characteristic properties of matter from the large-scale stability of matter to the existence of the periodic table of the elements. The Pauli exclusion principle is one of the most important principles in physics, primarily because the three types of particles from which ordinary matter is made- electrons, protons, and neutrons-are all subject to it consequently, all material particles exhibit space-occupying behavior.
4.4 Astrophysics and the Pauli principle.4.2 Solid state properties and the Pauli principle.