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modulus
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I worked out the Planck Black-Body Radiation Formula using Bose-Einstein Statistics, but I feel there is something conceptual I am missing here.
When Planck derived the formula, he started out with the Boltzmann distribution function, and assumed that there were discrete energy levels, instead of a continuous spread. That's it.
But Bose-Einstein statistics assumes that the particles which fill these energy levels (in this case, photons), are non-distinguishable. Yet when we proceed with that assumption, we end up with the Planck formula (only the density of states expression, which when multiplied by hv, gives the final expression).
So is making energy levels in the Boltzmann Distribution discrete somehow equivalent to assuming non-distinguishable particles? What am I missing here?
When Planck derived the formula, he started out with the Boltzmann distribution function, and assumed that there were discrete energy levels, instead of a continuous spread. That's it.
But Bose-Einstein statistics assumes that the particles which fill these energy levels (in this case, photons), are non-distinguishable. Yet when we proceed with that assumption, we end up with the Planck formula (only the density of states expression, which when multiplied by hv, gives the final expression).
So is making energy levels in the Boltzmann Distribution discrete somehow equivalent to assuming non-distinguishable particles? What am I missing here?