Derivation of Rayleigh–Jeans law

[jonathanpun]

I have read the derivation of the Rayleigh-Jeans law from:
http://www.cv.nrao.edu/course/astr534/BlackBodyRad.html

This derivation is quite similar to the derivation in my textbook.

My question is why the frequency/wavelength is quantized, but there still a d$\nu$ or d$\lambda$. Not this "d" only apply to continuous variables?

And since the frequency is quantized, that means the emission spectrum is not continuous? But my textbook said "condensed state emits a continuous spectrum of radiation."

 

[Bill_K]

It's the energy which is quantized, not the frequency. You can have a photon of any frequency. But then E = n hω

(Derivations of this and other formulas often work in a large box of side L for convenience, to help with the normalization. In a box of side L the wavelength must be a submultiple of L. Afterwards, however, you let L -> ∞, and this restriction disappears.)