Derivation for black body radiation. What is the 2 bout?

AI Thread Summary
The discussion centers on the derivation of black body radiation and the factors involved in calculating radiative energy density. The formula presented includes terms for energy density, energy of vibrating atoms, probability distribution, and the number of states, with a factor of two included to account for two perpendicular polarization modes of waves. The rationale for this factor is that each mode allows for independent energy shedding, akin to having two taps to drain a tank simultaneously. Participants seek clarification on the concept of polarization modes and how to prove their existence in the context of black body radiation. Understanding these principles is crucial for accurately defining the terms and equations involved.
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$${\rho}({\lambda}) d{\lambda}=E({\lambda})*f({E(\lambda}))*D({\lambda})d{\lambda}$$
$${\rho}({\lambda}) d{\lambda}$$ is density of radiative energy,
$$E({\lambda})= k_BT$$ is the energy of an atom vibrate in 3D,
$$f({E(\lambda}))=1$$ is the probability distribution. Equals to 1 because we follow equipartition theorem,
$$D({\lambda})d{\lambda}=2 *{\frac{4V\pi}{\lambda^4}}d{\lambda}$$ ,$$D({\lambda})d{\lambda}$$ is the number of state. And 2 there is because "Another technical problem is that you can have waves polarized in two perpendicular planes, so we must multiply by two to account for that. " from hyperphysics.

My question is : do I define every terms above correctly?
And I don't understand why wave polarize then we have to time two in the number of state? There will be double states because I the polarize wave are boson. But boson is not in classical.how do they so sure have to times two there?
Thanks.
 
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It sounds like you answered your own question: The factor of two comes about because there a two polarisation modes through which atoms can shed their energy. Like having two taps to empty a water tank.

Claude.
 
Claude Bile said:
The factor of two comes about because there a two polarisation modes through which atoms can shed their energy. Like having two taps to empty a water tank.

Claude.

Can you please explain more? How two taps to empty a water tank? Water go from taps to tank then?
How should I prove the two polarization modes? Please tell me. Thanks.
 
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