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 an be identified with any particular particle.

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.

Maxwell-Boltzmann distribution is used for solving distinguishable particle and Fermi-Dirac, Bose-Einstein for indistinguishable particles.