Kittel nearly free electron model

[ehrenfest]

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 $k = \pm \pi/a$ are not the traveling waves $\exp(i\pi x/a)$ or $\exp(i\pi x/a)$ 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

 

[genneth]

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?

 

[ehrenfest]

He is saying that it is only true for wavefunctions at $k = \pm \pi/a$.

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.

 

[ehrenfest]

anyone ?