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On the quantum theory of radiation 
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#1
Nov1912, 04:48 PM

P: 85

Hi,
In section 3 of Einstein's "On the quantum theory of radiation" Einstein says equations (8) and (9) follow from (7) and Wien's displacement law. I don't see how that is. For example, if we replace (8) by [tex] \frac{A_m^n}{B_m^n} = \alpha \frac{\nu}{T} \nu^3 [/tex] All conditions still seem to hold. What am I missing? Also, can somebody point me to a derivation of Wien's displacement law that does not assume Planck's formula? Thank you, A_B 


#2
Nov1912, 05:09 PM

Sci Advisor
Thanks
P: 4,160

He says A and B are constants which are "characteristic for the combination of indices considered". The indices referred to are ε_{m} and ε_{n}, the initial and final energy of the state, and in particular the energy difference ε_{m}  ε_{n}, that is, the frequency ν of the emitted radiation. They cannot depend on the temperature T. So the numerator A/B must be a function of ν only, and from Wien's Law it must be proportional to ν^{3}, giving us Eq 8.
Likewise from Wien's Law the denominator must be a function of ν/T, which implies Eq 9. 


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