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On the quantum theory of radiation

by A_B
Tags: quantum, radiation, theory
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Nov19-12, 04:48 PM
P: 85

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
\frac{A_m^n}{B_m^n} = \alpha \frac{\nu}{T} \nu^3
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,

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Nov19-12, 05:09 PM
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Bill_K's Avatar
P: 4,160
He says A and B are constants which are "characteristic for the combination of indices considered". The indices referred to are εm and εn, the initial and final energy of the state, and in particular the energy difference εm - εn, 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 ν3, 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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