# Solved: Kittel Problem 7.1 About Kinetic Energy in Square Lattice

• ehrenfest
In summary, the question is asking to show that the kinetic energy of a free electron at the corner of the first Brillouin zone in a simple square lattice is twice as high as that of an electron at the midpoint of a side face of the zone. The clarification is that the electron's k-vector should be at these locations in k-space, rather than in real space.
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."

?

## The Attempt at a Solution

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

## What is the Kittel problem?

The Kittel problem is a theoretical physics problem that involves calculating the kinetic energy of electrons in a two-dimensional square lattice. It was first introduced by physicist Charles Kittel in 1948.

## What is the importance of solving the Kittel problem?

Solving the Kittel problem allows us to better understand the behavior of electrons in a square lattice, which has important applications in various fields such as solid-state physics, materials science, and condensed matter physics.

## What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. In the case of the Kittel problem, it refers to the energy of electrons as they move through a square lattice.

## How is kinetic energy calculated in the Kittel problem?

In the Kittel problem, the kinetic energy is calculated using the equation E = (h^2/2m)(kx^2+ky^2), where h is Planck's constant, m is the mass of the electron, and kx and ky are the components of the electron's wave vector in the x and y directions, respectively.

## What are the applications of the Kittel problem?

The Kittel problem has applications in various fields such as understanding the behavior of electrons in metals, semiconductors, and other materials, as well as in the development of technologies such as transistors and computer chips.

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