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My book has a discussion of how the Bragg model can explain the origin of energy band gaps in solid. I have attached the relevant part of this discussion. I would very much like if someone could help me understand what it's basically trying to say.

Facts:

1) In the free electron model, the eigenstates of the hamiltonian are plane waves.

2) In the nearly free electron model we consider the free electron waves to be perturbed by a periodic potential.

But what does all this have to do with Bragg reflection? that is:

1) What are the electron waves scattering against?

2) I can see the Brillioun zone boundaries fulfill the Bragg condition so what happens to the electron waves physically at these points? And what happens for the electron waves not fulfilling the Bragg condition?

3) What does the book mean by the fact that the electron waves are standing waves at the zone boundary but not in general? How can a wave be standing at one point and moving at another?

Facts:

1) In the free electron model, the eigenstates of the hamiltonian are plane waves.

2) In the nearly free electron model we consider the free electron waves to be perturbed by a periodic potential.

But what does all this have to do with Bragg reflection? that is:

1) What are the electron waves scattering against?

2) I can see the Brillioun zone boundaries fulfill the Bragg condition so what happens to the electron waves physically at these points? And what happens for the electron waves not fulfilling the Bragg condition?

3) What does the book mean by the fact that the electron waves are standing waves at the zone boundary but not in general? How can a wave be standing at one point and moving at another?