0

I am reading Supplement #2 to Matter and Interaction book: Link

Below question is about potential energy.

In the paragraph labelled Energy Bands in Solids I am very clear what they mean of energy level of single atom. Energy level here is function of distance between nucleus and electron. Later they talk about energy levels in solids. Here is quotation:

If we assemble many such atoms to form crystalline solid, the electric potential energy of the solid is periodic in x (and y and z) with period corresponding to the distance between nuclei, as shown in Figure S2.2illustration

I cannot understand what is the distance in solids that we are measuring. Is it average distance between all nuclei and electrons or distance between one fixed nucleus and all electrons. Why is it periodic along only x, y, z? Would it be periodic if we travel along vector (1,1,1)?

user1700890
  • 155
  • The energy levels in an atom are not a function of the distance between the nucleus and electron. Why do think that they are? – mike stone Mar 04 '22 at 19:08
  • @mike this is what the very first paragraph says: We have typically plotted U as a function of r, the separation of nucleus and electron – user1700890 Mar 04 '22 at 19:14
  • 1
    Surely $U$ is the potential energy function, not the energy level? The energy levels themselves come from solving the Schrodinger equation for the potential energy function $U$. They are not a function of position. – mike stone Mar 04 '22 at 19:21
  • But they are a function of direction within the crystal, as shown on an $E$ vs $k$ diagram. – Jon Custer Mar 04 '22 at 19:32
  • @mikestone, thank you, I updated the question. – user1700890 Mar 04 '22 at 19:33
  • @JonCuster, I cannot find k, did you mean r? – user1700890 Mar 04 '22 at 19:33
  • $k$ is the crystal momentum. Energy levels in a crystal are Bloch states, extending throughout the crystal. Position is irrelevant, momentum is king. See, for example, https://physics.stackexchange.com/questions/320941/what-information-can-we-extract-from-the-electronic-band-structure for an $E$ vs $k$ band structure. The capital Greek letters on the x-axis are various high symmetry momenta directions. – Jon Custer Mar 04 '22 at 19:39

0 Answers0