Assumptions for derivation of Plancks' law

[tom.stoer]

What are the most general assumoptions for the derivation of Planck's law in quantum statistical mechanics:
- thermodynamical equilibrium
- non-interacting bose gas (photons)

Do I miss anything?

 

[unusualname]

Hi Tom,

you need to impose a discretization condition a la Bose in his ~1 page 1924 paper:

http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Bose_1924.pdf

"Let there be different species of quanta each characterized by the number N_s and energy hv_s"

edit: you may have meant this by "bose gas" in which case, no there are no further assumptions

 

[tom.stoer]

you need to impose a discretization condition

...

edit: you may have meant this by "bose gas" ...

yes, that's what I meant; thanks

are there examples for "fermionic radiation"? what about the neutrino spectrum from the sun? (OK, there's the problem that the neutrinos are not in equilibrium, but what would happen if they were? is there a similar derivation for a non-interacting fermi gas in thermodynamic equilibrium with fermionic radiation?)

 

[unusualname]

I guess that would require fermi-dirac statistics, but I don't know much about specific applications to neutrinos or other non-interacting fermion situations - probably worth a search in academic archives.