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I know that thermally excited materials "act as atomic oscillators" which can oscillate in a continuous range of frequencies, producing light in said frequencies. But in my searches, the nature of the oscillators isn't clear.

Are these quantum harmonic oscillators (i.e. each atom is a quantum oscillator)? If so, how is the frequency distribution continuous? And why is the energy of quantum oscillation related at all to the thermal energy distribution (Boltzmann distribution)?

In summary, what's the exact mechanism by which blackbody radiation is produced?

side question: I've read about the Bose-Einstein distribution for the blackbody spectrum, but don't understand much. How does that fit in here?

dkarkada
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Are these quantum harmonic oscillators (i.e. each atom is a quantum oscillator)?

You need to distinguish between the hot atoms of the blackbody and the electromagnetic radiation in free space.

The hot atoms are hard to describe quantitatively. Instead, the electromagnetic vibration modes in free space (the blackbody cavity) are easier to describe, and they can be treated as harmonic oscillators.

If so, how is the frequency distribution continuous?

When analyzing the electromagnetic waves within a finite volume $V$, you find a spectrum of discrete frequencies. (Think of the standing waves inside a rectangular box.) Only in the limit of an infinitely big volume ($V \rightarrow \infty$) you get a continuous spectrum.

And why is the energy of quantum oscillation related at all to the thermal energy distribution (Boltzmann distribution)?

The electromagnetic radiation is in thermal equilibrium with the hot atoms of the blackbody. Both have the same temperature $T$.

Thomas Fritsch
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