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

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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.

Comments

This video is really nice! Although it's not entirely clear the statement (9.1). could phi_k+G contain a phase factor?
Multiplication in spatial r domain becomes to Convolution in inverse lattice or k domain. Nothing but a Modulation.
Wonderful, Beautiful!
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?