Photons are Bosons, and so here are some links to the derivations of equations famous for the determination of photon energy distributions, most famous being Plank's and Wien's laws for black bodies that are applied to stars and fundamental (along with interferometery) for astrophysical studies:
Black Body radiation with Plank's law, Rayleigh-Jean's equations, links to derivations and applications!!!
Photon energy density, Bose-Einstein distribution, and density of energy states for black body radiation derived.
Most of the phenomenon of the world we touch is governed by fermion interactions, of particular importance has been the application of fermion statistics to solids, creating solid state physics, which underlies most all of sophisticated electrical engineering today.
Fermi Energy distribution of electrons, protons, and neutrons, the fermion which differs in that since ground states can hold a limited number of fermions, these states can be filled.......producing the n and p conducting states of conductors and semi-conductors.
Electron densities in solids are derived here, fundamental to theoretically understanding and calculationg conductivity in solids (and I used this concept as a limit for larger hydrocarbon molecules in a fluid (where I quasi-merged the wave functions of the individual atoms to understand why the "de Gaston Decharger" worked, my first patent [see my RESUME] Patent #3784876 Static Decharger, granted January 8, 1974).
Before quantum mechanics, Boltzman did the statistics for particles such as the molecules in a gas. The next two links will take you successively to the Boltzmann energy distribution (compare witht the Bose-Einstein and Fermi distributions of particles in energy-density distributions, and the key factor of the physical concepts of how the particles behave is found in the exponent containing expression in the denominator.