Identical Particle

Full Title or Meme

Two particles are considered identical when one cannot be distinguished from one another, even in principle.

Context

In Quantum Mechanics two particles (or two waves) that can be considered identical include, but are not limited to, elementary particles (such as electrons), composite subatomic particles (such as atomic nuclei), as well as atoms and molecules1,composite subatomic particles (such as atomic nuclei), as well as atoms and molecules. For example, all of the electrons bound to an atom are indistinguishable and so there is no set of state variables that can be identified with a particular electron.

In statistical mechanics

Assume you have two particle A and B in states 1 and 2. If the two particle are distinguishable, then by exchanging the particles A and B, you will obtain a new state that will have the same properties as the old state i.e. you have degeneracy and you have to count both states when calculating the entropy for example. On the other hand, for indistinguishable particles, exchanging A and B is a transformation that does nothing and you have the same physical state. This means that for indistinguishable particles, particle labels are unphysical and they represent a redundancy in describing the physical state and that is why you would have to divide by some symmetry factor to get the proper counting of states.

Solutions

For this page the distinction that is important in the statistical rules that apply. Maxwell-Boltzmann distribution is used for solving distinguishable particle and Fermi-Dirac, Bose-Einstein for indistinguishable particles.

Particles which exhibit symmetric states are called bosons. The nature of symmetric states has important consequences for the statistical properties of systems composed of many identical bosons. These statistical properties are described as Bose–Einstein statistics.

Particles which exhibit antisymmetric states are called fermions. Antisymmetry gives rise to the Pauli exclusion principle, which forbids identical fermions from sharing the same quantum state. Systems of many identical fermions are described by Fermi–Dirac statistics.