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
As
, there are two fundamentally different kinds of solutions,
namely
and
.
The symmetric solution describes particles that are called bosons.
Particles that are described by the antisymmetric solution 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.