Kittel nearly free electron model

In summary, the conversation is about a question regarding a section in Kittel's solid-state physics book. The question is about the 1D example on pages 164-165 and the confusion about wavefunctions at k = \pm \pi/a. The person asking for help is unsure about the explanation given by Kittel and wonders how he knows that the wavefunctions will bounce back and forth between k = \pm \pi/a by Bragg reflection. Another person suggests that Kittel is simply stating that electrons in a lattice are not free. The original person asks for help from someone with access to the book since they are having trouble understanding the material.
  • #1
ehrenfest
2,020
1

Homework Statement


This question refers to Kittel's solid-state physics book.

I just do not understand the 1D example on pages 164-65. So, I understand everything until the line "The wavefunctions at [itex]k = \pm \pi/a[/itex] are not the traveling waves [itex]\exp(i\pi x/a)[/itex] or [itex]\exp(i\pi x/a)[/itex] of free electrons."

Kittel tries to explain, but I just don't understand. Is he saying that they will just bounce back and forth between k = pi/a and k = -pi/a by Bragg reflection? How does he know that??!? PLEASE HELP!

Homework Equations


The Attempt at a Solution

 
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  • #2
I'm afraid I don't understand what you don't understand. Isn't he just stating that electrons in a lattice aren't free?
 
  • #3
He is saying that it is only true for wavefunctions at [itex]k = \pm \pi/a[/itex].

genneth, do you have the book? If not then it will be hard to answer this question since I really don't understand like half a page after that and a figure on the previous page.

But thanks for your effort.
 
  • #4
anyone ?
 

What is the Kittel nearly free electron model?

The Kittel nearly free electron model is a simplified theoretical model used in solid state physics to describe the behavior of electrons in a crystal lattice. It assumes that the electrons are nearly free to move in the crystal, with only weak interactions between them and the lattice ions.

How does the Kittel nearly free electron model differ from the band theory of solids?

The Kittel nearly free electron model is a simplified version of the band theory of solids, which takes into account the interactions between the electrons and the lattice. In the Kittel model, these interactions are assumed to be weak and can be neglected, resulting in a simpler mathematical description.

What are the assumptions of the Kittel nearly free electron model?

The main assumptions of the Kittel nearly free electron model are that the electrons are free to move in the crystal lattice, there are only weak interactions between the electrons and the lattice ions, and the electrons are described by plane waves with well-defined energies and momenta.

What are the limitations of the Kittel nearly free electron model?

The Kittel nearly free electron model is a simplified model and therefore has some limitations. It does not take into account the effects of electron-electron interactions, which can be significant in certain materials. It also does not consider the effects of impurities or defects in the crystal lattice.

What are some applications of the Kittel nearly free electron model?

The Kittel nearly free electron model is commonly used in the study of metals, where the interactions between the electrons and the lattice are weak. It is also used in the study of semiconductors, where the electrons behave like free particles in the conduction band. Additionally, the model is used in the development of electronic devices and materials with specific electrical and magnetic properties.

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