Undergraduate phys here, inb4 /x/ Can someone explain pic-related

>>8319082
Wish I could help you OP. I studied this stuff like 3 years ago and have long forgotten it.

You are trying to represent a lattice structure in some way where the distance between each atom is 'a' length apart from its neighbor.

Sorry OP.

>>8319149
yeah exactly, only this is the reciprocal or something
and wow I'm amazed that you've forgotten it, did you continue in physics or did u go into a different direction?

File: wavevector.jpg (21KB, 374x616px) Image search: [Google]

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>>8319082
Yes k is the wavevector, its absolute value represents the inverse of the spatial periodicity of your wave (by a factor 2pi).
So k = 0 or 2pi/a represents a uniform shift of your whole lattice in one direction. In other word, fucking nothing, which is why the energy is 0.
k = pi/a is the maximum deformation of adjacent nodes of your lattice

see pic related

>>8319237
ah so k is like the displacement from equilibrium?
and it is represented by momentum (k) because that's how much momentum it has when displaced that far?

I find it weird that the top part of my image is there, according to your explanation only the bottom waves should be in my picture... but according to mine the deformation goes past k=pi/a

>>8319256
>ah so k is like the displacement from equilibrium?
No it's the inverse of the periodicity, multiplied by pi.
The curves I'm showing you are a real space representation of the wave, not the dispersion relation.

Did you have your class on Fourier transforms yet?

>>8319265
You're saying k is just a mathematical definition.
or is it more like frequency, because that increases too in your pic. I've had this definition so many times: optics, structure of matter, statistical but it's so abstract. And then why is that top part of my pic still there?

Yes I've had fourier transforms. They translate the frequencies that make up a signal (related to power) to the actual wave function (related to power) so you can tell which frequency has for example the highest power
thanks for your help

ok I get k now, still don't get that upper part of my pic

>>8319276
>or is it more like frequency
yes, except with space instead of time
>because that increases too in your pic
no. Careful not to mix frequency and spatial frequency. One is time, one is space.

>>8319404
so if k is spatial frequency (in radians using 2pi) then why does it mean that you shift the whole lattice in one direction when you have an angular spatial frequency of 2pi/a

File: wavevector.jpg (24KB, 374x616px) Image search: [Google]

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>>8319431
Because the continuous wave function is one thing, but in reality there are only discrete atoms moving
see pic

>physics
>>>/x/

>>8319431
ok then somehow physicists deem it understandable to do this in the k notation and not the real space... I understand that now thanks: they use a wave to represent the deformation of nodes... which is weird but ok
and what is on the y-axis then? potential energy for the lattice which wants to move back (like a spring)?
if yes then I get your explantion except the upper wave still :)

^
I meant to quote >>8319431

>>8319445
goddamnit Im retarded I MEANT TO QUOTE THAT POST

We have a set of atoms on a lattice. If the lattice spacing is infinite, then the Hamiltonian should just reproduce the spectrum of the individual atoms. As the atoms are brought closer together, the atomic orbitals hybridize and allow for hopping between atoms and mixes the atomic orbitals. This leads to avoided crossings where "bands" of one atomic orbital intersect those of another and leads to the general band-diagram of whatever solid you are looking at. If you wand a much better description, I would suggest looking into density functional theory since that is generally how these band structures are calculated in modern times. There were also a bunch of papers in the early 20th century which looked at the process exactly as I have described it, but fuck if I can remember any of them. I think if you look at some of the really early work on Tamm states and the like you will probably find them..

File: Bloch_function.svg.png (38KB, 765x333px) Image search: [Google]

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>>8319489
>what is on the y-axis then
Well it depends what you're talking about. Mechanical waves? Electromagnetic waves? It can be a physical displacement, or a potential, either way the theory is the same.

>the upper wave
Not the upper wave, the upper waveS. There are an infinity of those. A wave function in a lattice is of the form [math]e^{i\mathbf{k \cdot r}}u(\mathbf{r})[/math]
where u is a function periodic over the lattice. In that case k is the wavevector, and the different possible u have different energies, for the same wavevector. The lowest energy state is for u = constant. The second energy state is probably for something that looks like u(r) = sin(2pi r/a) (in an empty lattice). Higher energy states have more and more nodes.

>>8319562
why does this shit have to be so fucking complicated?
can't they just put it in real space

>>8319673
does the pic in >>8319562 look simpler to you? It's in real space.

>>8319697
what is that dashed wave? the electron wave? and that dark black line is it fourier transform?
it looks okay but I don't know what it's saying. I must visualize an electron going towards one of those ions right? why is that wave like it is? Sometimes it crosses an ion, and sometimes it doesn't until the 4th ion from the left on that picture