Statistics
The concept of statistics is related to the behaviour of large number of particles. For instance, Maxwell-Boltzmann statistics works well in the classical physics, while describing the distribution of energy among the molecules of a gas. However, in quantum physics, two new forms of statistics have been developed which are the Bose-Einstein statistics and the Fermi-Dirac statistics. These statistics reflect in the behaviour of wave function describing systems of identical particles under their interchange.
Bose-Einstein Statistics
If the particles have integral spins, i.e. 0, 1, 2, ..., they are known as Bosons, e.g. photons, pions, etc. The wave function of the system consisting of Bosons is symmetric when we interchange any two identical Bosons, i.e. ψ(x1, x2) = ψ(x2, x1). Similar results can be written for more than two particles.
Fermi-Dirac Statistics
The particles having half integral spins are known as Fermions. Examples are protons, neutrons, etc. All Fermions obey Pauli's exclusion principle. The wave function of a fermion system is antisymmetric under interchange of two identical particles, i.e. ψ(x1, x2) = -ψ(x2, x1).