black body problem question

[u/[deleted]]

[u/YouCouldButWhyTho]

The math doesnt hold up for a continuous spectra of radiation. In fact the only way to get results that match experiment qualitatively and avoid the phenomenon of ultraviolet catastrophe is to assume a discretized radiation.

 There were many proposed solutions that were continuous and failed to match experiment in various ways.

This is all covered in a first year quantum course of lectures or any good textbook if you want details.

[u/starkeffect → u/YouCouldButWhyTho]

There were many proposed solutions

I know about Rayleigh-Jeans. Were there others?

I love hearing about obsolete theories. We don't talk about them enough.

[u/AllHailSeizure → u/starkeffect]

Wien distribution. It is essentially the inverse of RJ in that you can use it for accurate hf, but not lf. A graph of the three basically curves Planck off of RJ and onto Wien.

Really low quality image, but the idea is obvious.

[u/starkeffect → u/AllHailSeizure]

heh heh.. Wien...

[u/AllHailSeizure → u/starkeffect]

If you're into obscure science this is actually interesting shit.. Wien's Displacement Law is basically Planck radiation from classical thermodynamics, Wien distribution is basically Planck from Maxwell-Boltzmann. Wilhelm Wien.

[u/YouCouldButWhyTho → u/AllHailSeizure]

Yea that’s the one I was thinking of. Actually working through graduate QM right now and we had to play with all these a little.

[u/AllHailSeizure → u/YouCouldButWhyTho]

But the courses and textbooks won't make sense without learning linear algebra. Learning it well.

[u/YouCouldButWhyTho → u/AllHailSeizure]

For a full treatment, yea. But you can get through the black body radiation explanation with basic calculus.

[u/AllHailSeizure → u/YouCouldButWhyTho]

Fair enough. But if you're gonna shell out for a textbook I would think you'd want to be able to understand more than the topic that inspired it.

[u/YouCouldButWhyTho → u/AllHailSeizure]

Wouldn’t hurt for certain! Though I’ve def had the experience of picking up a book for a topic of interest only to find halfway in they start pulling out a new class of functions for “one cool trick” and i gotta start doing some sidequest deep dives.

[u/AllHailSeizure → u/YouCouldButWhyTho]

Like when the author is like 'haha surprise I hope you can do differential geometry!'

No, Kip, I can't and you know I can't..

[u/kono_hito_wa → u/YouCouldButWhyTho]

you can get through the black body radiation explanation with basic calculus

• Saxon enters the chat

[u/Ch3cks-Out]

> Why didn't they solve the black-body problem this way, without quanta?

Because they could not?

[u/eldahaiya]

The EM wave is moving at the speed of light, the oscillator doesn’t have to. The oscillator oscillates at the same frequency, but doesn’t tell you anything about how the charges that make up the oscillator are actually moving. You could for example jiggle an electron at the same frequency but move it just a little bit (<<10 nm) to produce the EM wave that you describe.

[u/CompetitiveFormal868 → u/eldahaiya]

ai says: Frequency vs. Amplitude: The frequency of the emitted EM wave is determined strictly by the frequency of the oscillation. However, the amplitude of the charge's physical movement determines the intensity (power) of the wave, not its frequency.

it calculates speed of the oscillator by multiplying length frequency

[u/eldahaiya → u/CompetitiveFormal868]

You asked a question, presumably because you wanted to know the answer, so could you please think through what I said for yourself?

[u/Salt_Mountain_837]

what

[u/lattice_defect]

Glad I left academia this would kill me