Recent content by NCD135

Thanks! This makes sense to me. Now I see the contradiction and can believe that it is more accurate to view the band as "literally continuous" than "technically discrete but effectively continuous."

PS I'm not trying to counter any of your points! I'm just trying to explain my confusion, because I know that you are correct, and I want to understand why!

I would answer yes to both of those questions. Griffith's Quantum Mechanics writes it as: "Evidently there are N states in each band, so closely spaced that for most purposes we can regard them as a continuum." You have the boundary condition that ψ(x+Na) = ψ(x), which quantizes the crystal...

Hahaha. I'm not that crazy. I've taken classes/I read Kittel. Sometimes when I have a question like the above, my friends can't answer either, so I turn to the forums ;) Can you help with this particular confusion? I can "derive" band theory (e.g. Nearly free electron model or Kronig-Penny)...

I would have interpreted this thread https://www.physicsforums.com/threads/conservation-of-energy-with-non-allowed-states.787232/#post-4943724 to say more or less exactly what I am describing.

Okay, so I have some sort of fundamental misunderstanding here. I was taught that, at any given point in space, all an electric field can do is shift all of the energy levels by a constant. Even within a band, there are still technically discrete allowed energies. Therefore, absent small thermal...

Okay, so I have some sort of fundamental misunderstanding here. I was taught that, at any given point in space, all an electric field can do is shift all of the energy levels by a constant. Even within a band, there are still technically discrete allowed energies. Therefore, absent small...

Hi Simon, I understand that much. My title might be misleading, but I hope my post was a little more clear about that! My question is much more subtle. In insulators, the bands do not overlap and the gap is so large no thermal fluctuation can allow move to higher kinetic energy states...

I almost "get" it, but not quite. Can someone help? Here is my current understanding. Say you solve the Kronig-Penny model. You find that you get bands of N closely spaced energy levels, with large gaps between them. Under normal conditions, electrons fill the band to some level (let's say we...