Statistical Laws

In determining the statistical behavior of particles, we must consider the laws that the particles obey. There are three distribution laws determining the distribution of particles among available energy states.

One distribution law is the Maxwell-Boltzmann probability function. In this case, the panicles are considered to be distinguishable by being numbered, for example, from 1 to N. with no limit to the number of particles allowed in each energy state. The behavior of gas molecules in a container at Fairly low pressure is an example of this distribution.

A second distribution law is the Bose-Einstein function. The panicles in this case are indistinguishable and, again, there is no limit to the number of particles permitted in each quantum state. The behavior of photons, or black body radiation, is an example of this law.

The third distribution law is the Fermi-Dirac probability function. In this case, the particles are again indistinguishable, but now only one particle is permitted in each quantum state. Electrons in a crystal obey this law. In each case, the particles are assumed to be noninteracting.