ABSTRACT
In this section, we are concerned with systems consisting of particles with negligible mutual interaction, that is, ideal gases. Let us first consider a classical case where the particles are considered distinguishable. For this classical description, no symmetry requirements are imposed on the wave function when two particles are interchanged and any number of particles can be in the same single particle state, say, k. In this case the particles are said to obey Maxwell–Boltzmann statistics (abbreviated MB statistics). In the real world, however, identical particles are indistinguishable, so a quantum treatment is more correct. Usually, however, MB statistics is applied to systems that are nondegenerate, meaning the density of particles is so low that their quantum wave functions have insignificant overlap. Then it is unlikely that any two particles can even be in the same single-particle quantum state, and quantum symmetry constraints are not necessary.
