A problem with a figure related to band theory

In summary, the conversation discusses a diagram showing the introduction of band theory in solid state physics. It is explained that the diagram is a common way of visualizing the concept, with part (a) representing single atom states and part (b) representing multiple atoms in a lattice. However, there is concern about the accuracy of part (b) as it appears to show a mix of twofold and fourfold splitting, and suggests that the ground state does not suffer any splitting.
  • #1
DaTario
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TL;DR 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

DaTario
 
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  • #2
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
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
 
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  • #4
Dr Transport said:
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
Gordianus said:
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
It does indeed look wrong, each single particle state should split into as many states as there are particles in the system.
 
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FAQ: A problem with a figure related to band theory

1. What is band theory?

Band theory is a concept in physics that describes the behavior of electrons in a solid material. It explains how electrons move through a material and how they contribute to its properties.

2. What is a figure related to band theory?

A figure related to band theory is a visual representation of the energy levels of electrons in a solid material. It often shows the energy bands and band gaps of a material, which are important in understanding its electronic properties.

3. What is a problem with a figure related to band theory?

A problem with a figure related to band theory could be a mistake in the data or calculations used to create the figure, or an error in the figure itself. It could also be a discrepancy between the figure and the theoretical predictions of band theory.

4. How can a problem with a figure related to band theory be resolved?

To resolve a problem with a figure related to band theory, the data and calculations used to create the figure should be carefully checked for errors. If an error is found, it should be corrected and the figure should be updated. If there is a discrepancy between the figure and theoretical predictions, further research and experimentation may be needed to understand and resolve the issue.

5. Why is it important to address a problem with a figure related to band theory?

It is important to address a problem with a figure related to band theory because it could impact our understanding of the electronic properties of a material. If the figure is incorrect or misleading, it could lead to incorrect interpretations and conclusions about the behavior of electrons in the material. Addressing and resolving the problem is crucial for accurate and reliable scientific research.

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