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?
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
Only REAL explanation on the whole of youtube. Fuckin ace!
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!
Thank you so much for this. I have an incoming exam. This helps a lot.
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?
I was wondering how at min @, you went from having C_k in the potential term to C_(k-G). Thank you!
For anyone searching for the reference at 5:56 it is video 5-4
The guy sounds like Jack from Jack-in-the-Box lol. Good video!!
Can someone explain what is the meaning of a k point?
Wonderful, Beautiful!
Multiplication in spatial r domain becomes to Convolution in inverse lattice or k domain. Nothing but a Modulation.
This was very helpful. thanks a bunch :)
Did you meant...thanks a BLOnCH
I had to xD
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??
Because we have sum over G vectors, vec(g1) is one vector and Vec(-g1) is other.
This video is really nice! Although it's not entirely clear the statement (9.1). could phi_k+G contain a phase factor?
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
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.
Too fast. Annoying.