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ehrenfest

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**[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."

?