Quantum Mechanics
Identical particles: Introduction

Identical particles cannot be distinguished by means of any intrinsic properties. This can lead to effects that have no classical analog. Two particles are identical if there are no interactions that can distinguish them. Therefore a physical observable must be symmetrical with respect to the interchange of any pair of two particles. The time-dependent Schrödinger equation for two identical particles is

Time-dependent Schroedinger equation for two identical particles

As H (r1,r2) = H (r2,r1), there are two fundamentally different kinds of solutions, namely Psi (r1,r2) Psi (r2,r1) and Psi (r1,r2) = - Psi (r2,r1). The symmetric solution Psi (r1,r2) Psi (r2,r1) describes particles that are called bosons. Particles that are described by the antisymmetric solution Psi (r1,r2) = - Psi (r2,r1) are called fermions. Electrons, protons and neutrons are fermions, and photons and pions are bosons. Atoms, being aggregates of tightly bound particles, are either fermions or bosons. Particles with integer spin are always bosons while particles with half-integer spin are always fermions.