Solved: Kittel Problem 7.1 About Kinetic Energy in Square Lattice

[ehrenfest]

[SOLVED] kittel problem 7.1

Homework Statement

This question relates to Kittel's solid-state physics book. I have the 8th edition.

In this question, he says:

"Show for a simple square lattice (two dimensions) that the kinetic energy of a free electron at a corner of the first (I assume Brillioun is missing) zone is higher than that of an electron at the midpoint of a side face of the zone by a factor of 2."

But I thought you only discussed Brillioun zones in relation to k-space, not real space? It makes absolutely no sense to me to say that an electron is at a location in the first Brillioun.

Should this question really be:

"Show for a simple square lattice (two dimensions) that the kinetic energy of a free electron whose k-vector is at the corner of the first (I assume Brillioun is missing) zone is higher than that of an electron whose k-vector is at the midpoint of a side face of the zone by a factor of 2."

?

Homework Equations

The Attempt at a Solution

 

[malawi_glenn]

Yes the question is to be understood that way :-)