Solid State Physics in a Nutshell: Topic 9-1: Bloch Theorem and the Central Equation

We start by introducing Bloch's theorem as a way to describe the wave function of a periodic solid with periodic boundary conditions. We then develop the central equation and find a relation between the Fourier coefficients associated with the wave vectors, k minus G, over all space.

[@g0rthaur]

Thank you for your effort and uploading this video to make it public for a world wide audience, it really helped me studying for my exam!

[@Moeman-mf5yq]

Only REAL explanation on the whole of youtube. Fuckin ace!

[@christianmaestre111]

Thank you so much for this. I have an incoming exam. This helps a lot.

[@thedomestomp]

The guy sounds like Jack from Jack-in-the-Box lol. Good video!!

[@irenevillarrodriguez622]

I was wondering how at min @, you went from having C_k in the potential term to C_(k-G). Thank you!

[@minhokim8263]

Wonderful, Beautiful!

[@elahehakhoundi7570]

This was very helpful. thanks a bunch :)

[@xgozulx]

Did you meant...thanks a BLOnCH I had to xD

[@minhokim8263]

Multiplication in spatial r domain becomes to Convolution in inverse lattice or k domain. Nothing but a Modulation.

[@ProfessorKInGkiWI]

For anyone searching for the reference at 5:56 it is video 5-4

[@robertfennis6088]

8:20 I looked at solutions of wave equations at band edges but I consistantly find that the solutions of the bloch functions for k+G are very different. Which should make sense because these eigen states have different energies. However, since I doubt that I am discovering A fundamental flaw in QM, I guess my reasoning is wrong. Could you help me?

[@asaf2323]

Can someone explain what is the meaning of a k point?

[@alaaakkoush1135]

In 6:43, why should we care about C of k+g1 , if the central equation only has C of k and C k-g1??

[@amanpawar_ap]

Because we have sum over G vectors, vec(g1) is one vector and Vec(-g1) is other.

[@aitorgarcia1147]

This video is really nice! Although it's not entirely clear the statement (9.1). could phi_k+G contain a phase factor?

[@aitorgarcia1147]

For instance, if you chose a planewave as your phi_k(r)=exp(ikr), then phi_k_G(r)=exp(i(k+G)) clearly introduces the phase factor exp(iGr), which in principle is only when r is a translation vector T

[@amanpawar_ap]

the bloch wave function is u_k(r).exp(ikr) not just planewave exp(ikr). The results in this video are explicitly only for bloch case.

[@AbdolazimHasseli]

Too fast. Annoying.