Indistinguishable particles in quantum mechanics: an introduction

In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, the Pauli Exclusion Principle, or in general, the Symmetrization Postulate. Then, we introduce fermions and bosons and the distributions respectively describing their statistical behaviour in indistinguishable situations. Following that, we discuss the spin-statistics connection, as well as alternative statistics and experimental evidence for all these results, including the use of bunching and antibunching of particles emerging from a beam splitter as a signature for some bosonic or fermionic states. 1 An Extra Postulate is Required I believe most physicists would consider that the postulates (or at least the properties they embody) concerning the superposition, evolution and measurement of quantum states cover the essence of Quantum Mechanics, the theory that is at the basis of current fundamental Physics and gives us such an accurate description of Nature at the atomic scale. Yet, if the theory was only based on these postulates (or properties), its descriptive power would be almost zero and its interest, if any, would be mainly mathematical. As soon as one wants to describe matter, one has to include an extra postulate: Pauli’s Exclusion Principle. One of its usual formulations, equivalent to the one proposed originally by Wolfang Pauli in 1925 [1], is the following: Pauli’s Exclusion Principle — No two electrons can share the same quantum numbers.