What's going on in here?

Someone teach me path integration.

heheh

@ACuriousMind You like stellar physics right?

@SirCumference I have no idea what gave you that idea :P

I have 1315 answers on this site and only a single one of them is in the astrophysics tag

Though I could've sworn I asked you about neutrons stars at one point

Oh, I might be able to say something about neutron stars. That doesn't mean I like them or find them particularly interesting :P

But...but how

They're spheres of neutron degenerate gas, with masses comparable to the Sun but radii less than a city

It doesn't get more extreme than that...

@ACuriousMind Would you be mind helping me with a quantum problem?

Depends on the problem ;)

I have to find the power absorbed by a cube made of cubic crystal, whose unit cell contains an electron. In the question, it states that the "line shape function is normalized to unity and is rectangular with $10^9$ Hz width$

Is this line shape function a transition probability? All I can find online does not give me a clear understanding

(We know additionally the electrons have a Boltzmann distribution and don't obey the exclusion principle, if its relevant)

I have no idea what a line shape function is. I had half a semester's worth of condensed matter physics and the prof was terrible.

Mine didn't mention the term once in his class. Go figure

I would guess it describes the, well, shape of some sort of emission/absorption line here

generically, such a function would be intensity vs. frequency or wavelength, but what transition is meant in this case I do not know

I was thinking it could be something like that. But I thought that the emission/absorption would have to be a sinc-type function, through time dependent perturbation.

I suppose it could be some kind of intensity or something

@Argon emission lines are surely not always sinc functions. Often they are to good approximation Lorentz (aka Cauchy aka Breit-Wigner) shaped, for example

For the case of a sinusoidal EM wave incident I thought it had to be the case.

At any rate, assuming a rectangular absorption pattern, the frequency of the EM field is a single frequency. Why does the broadband line shape play a role at all?

I am guessing it might had to do with the total power absorbed will depend on what photons can match the lattice spacing or something

Also isn't a reactangular profile means you have a broad band of the same intensity?

@Secret I assume so. We never learned about lattice spacing in class, but given how nuts the class was, it could be possible