Kittel nearly free electron model

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Homework Help Overview

This discussion revolves around the nearly free electron model as presented in Kittel's solid-state physics book, specifically focusing on the interpretation of wavefunctions in a one-dimensional lattice context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the implications of wavefunctions at specific k-values and questions the nature of these wavefunctions compared to free electrons. Other participants raise points about the distinction between free electrons and those in a lattice, while also expressing confusion regarding the text's explanations.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the original poster's confusion regarding the text. Some guidance has been offered, but there is no clear consensus on the interpretation of the material, and further exploration of the topic is evident.

Contextual Notes

Participants note that understanding may be limited by the original poster's access to the book and the complexity of the material discussed, particularly in relation to figures and explanations provided in the text.

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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

 
Last edited:
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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?
 
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.
 
anyone ?
 

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