Why is it interesting?

Distribution functions describe the energies of particles in a system depending on its temperature. Even in systems which appear to be at a single temperature, such as the particles in air, some will be moving faster or slower than others. Understanding the distribution function is important for evaluating microscopic and macroscopic properties of a thermodynamic system.

Layman?

Student

Three of the most important examples of distribution function are the Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distributions; the former is a classical distribution, appropriate for identical but distinguishable particles, and the latter two are quantum distributions, used for fermions and bosons respectively.

• https://physics.stackexchange.com/questions/210552/what-really-is-a-dirac-delta-function/210557#210557

Researcher

• DISTRIBUTION FUNCTIONS IN PHYSICS: FUNDAMENTALS by M. HILLERY et. al.

Does the notion "Dirac Delta Function" make any sense?

Yes, have a look at this article.

Examples

Example1

Example2:

History