The emission spectrum of the black body. Woki has a nice derivation, and the first 80% is just combinatorics/. Botzmann started it by writing the combinatoric of an ideal gas at equilibrium in a container. If the gas of assumed to know pi accurate enough, then we get the Euler condition being me, we can approximate the histogram to an exponential equation in euler's number. This is the sphere packing assumption,. and it yielded the proverbial PV=nRT.
Since light wave and particle are dual, one can be solve in term of the other, Planck tried the same trick with a box full of photons. But he required the photons be quantized, they interact just a bit to meet the boundary condition,. where temperature equilibrates.. Internal, the photons do not interact, Boltzmann had them bounce like perfect spheres. Quantize is equivalent to having an integer metric space sufficiently accurate to planks uncertainty, quants of uncertainty.
He gets the energy density which transforms to spectral density in sphere packing world. Emission spectra is spectral density factored, sort of.
The point is, most of that was just combinatorics, how many ways can n things be selected from N things. Then we introduce bound system uncertainty, Plancks constant.
Wiki did a good job, educated me.
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