Exercise 2.1-1

Quick Questions to:

2.1 Basic Band Theory

Here are a few quick questions to 2.1.1: Essentials of the Free Electron Gas
What happens, if you do not choose U = U0 = 0 but U = U1 ?
What does the sentence "...a plane wave with amplitude (1/L)3/2 moving in the direction of the wave vector k" mean"? Wave vectors, after all, are defined in reciprocal space with a dimension 1/cm. What, exactly, is their direction in real space?
Recount what you know bout the spin of an electron.
Where does the (1/L)3/2 in the solution come from? What would one expect for a crystal woth the dimension Lx, Ly, Lz?
What kind of informarion is contained in the wave vector k?
Consider a system with some given energy levels (including possibly energy continua). Distribute a number N of classical particles, of Fermions and of Bosons on these levels. Describe the basic priciples.
How does on always derive the density of states D(E)?
     
Here are a few quick questions to 2.1.2: Diffraction of Electron Waves
Consider a fcc and bcc lattice with lattice constant a = 0.3 nm. Give the distance between {100} planes and the distance between the corresponding atomic planes. Do the same thing for the {111} plane of a fcc lattice with just one atom in the base and for a diamond structure.
Remember the Ewald construction? Describe and explain for what kind of situations it is particularly useful.
Compare the free electron model with and withour diffraction.
     
Here are a few quick questions to 2.1.3: Energy Gaps and General Band Structure
Draw a one-dimensin realistic periodic potential Niow draw in the first Fourie component. Add the probabiltiy densities for finding electrons with k = kBZ. Explain the energy splitting and why DE is approximately given by the first Fourier component of the potential.
     
Solution

Zum Index Zum Index

gehe zu 2.1.1 Das Bindungspotential

gehe zu 2.1.2 Bindungspotentiale, Federn, und der Elastizitätsmodul

gehe zu 2.1.3 Bindungspotentiale und weitere Eigenschaften

gehe zu 2.1.4 Vom Bindungspotential zum Kristall

gehe zu 2.1.5 Merkpunkte zu Kapitel 2.1

© H. Föll