A problem with a figure related to band theory

  • I
  • Thread starter DaTario
  • Start date
  • #1
922
29
Summary:
Hi, All, I would like to know the following figure is ok in the context of explaining to beginers the theory of bands (solid state physics).
Hi, All. In searching for images related to the introduction of band theory in solid sate physics I found this one:
1632510900492.png


I would like to ask you if I am correct in thinking the increase in the number of splittings (in b) is misleading to students.

Thank you all
Best regards,
DaTario
 
Last edited:

Answers and Replies

  • #2
Dr Transport
Science Advisor
Gold Member
2,517
639
First: where did you get this diagram?

Ok, now on to an explanation:
Part (a) looks like a set of single atom states.
Part (b) is for multiple atoms in a lattice, looks like two.
Part (c) is for a many atom lattice
 
  • #3
417
95
These kind of drawings are quite common and I've seen them in several books. The "idea" is that you start with a single atom and you have the standard atom energy levels (drawing a). With two close atoms we must split the atom levels to satify Pauli's principle (the splitting is shown very large to ease reading, drawing b). You keep adding many, many atoms until the discrete energy levels split in so many levels that the system looks like a continuum (drawing c). Kittel's or Ashcroft's books take this approach to introduce the subject
 
  • #4
922
29
First: where did you get this diagram?
Thank you for the answers.

I got it from image googling with key word "band theory solid state physics".

It seems that (b) shows neither a twofold splitting nor a fourfold splitting. So it seemed confusing to me.
 
  • #5
922
29
These kind of drawings are quite common and I've seen them in several books. The "idea" is that you start with a single atom and you have the standard atom energy levels (drawing a). With two close atoms we must split the atom levels to satify Pauli's principle (the splitting is shown very large to ease reading, drawing b). You keep adding many, many atoms until the discrete energy levels split in so many levels that the system looks like a continuum (drawing c). Kittel's or Ashcroft's books take this approach to introduce the subject
I understand it. I am worried with the drawings in (b), because it seems to show in one figure a mix of a twofold and a fourfold splitting.

It also bothered me that the figure also suggests that the ground state does not suffer any kind of split.
 
  • #6
697
147
It does indeed look wrong, each single particle state should split into as many states as there are particles in the system.
 

Related Threads on A problem with a figure related to band theory

  • Last Post
Replies
3
Views
915
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
939
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
1
Views
901
  • Last Post
Replies
6
Views
23K
Replies
2
Views
902
Replies
2
Views
955
  • Last Post
Replies
1
Views
3K
Top