## Study Guide for Quiz 1

The purpose of the quiz is to get you started in studying for the exam. The questions on the quiz will be short answer/calculation based on the most important parts of each chapter that we have covered. Here is checklist of things to study:

1. Chapter 1 - Drude theory
1. What is the Drude model for metals?
2. Calculate the conductivity in the Drude model (see HW problem).
2. Chapter 2 - Sommerfeld theory
1. How does the Sommerfeld model differ from the Drude model?
2. Express the density, Fermi velocity, and Fermi energy in terms of the Fermi wavevector in different dimensions.
3. What a typical Fermi energy in eV and kB T?
4. What is the density of states? What is the density of states in different dimensions for free electrons?
5. Explain the idea behind the Sommerfeld expansion.
6. How does the specific heat of metals depend on temperature?
3. Chapter 4 - Crystal lattices
1. What is a Bravis lattice?
2. What are simple cubic, face center cubic, and body center cubic lattices? Give basis vectors for each.
3. What is a primitive unit cell? a Wigner-Seitz cell?
4. Give some examples of lattices that can not be described as a Bravais lattice, but can be described by a lattice with basis. What is a lattice with basis?
4. Chapter 5 - Reciprocal lattice
1. What is the definition of a reciprocal lattice?
2. What is the reciprocal lattice of SC, FCC, and BCC lattices?
3. Know how to compute a basis for a reciprocal lattice.
5. Chapter 6 - X-ray scattering
1. Why are X-rays (and not for example visible light) useful for determining crystal structure?
2. What are the Bragg and Von Laue formulations of X-ray diffraction?
3. Explain the Ewald construction.
4. What are the Laue method, the rotating crystal method, and the powder method for X-ray scattering?
5. What is the structure factor for a lattice with basis? How does it effect X-ray scattering?
6. Chapter 8 - Electrons in a periodic potential
1. Give two equivalent statements of Bloch's theorem.
2. What is the velocity of an electron in a periodic potential?
3. What is the periodicity of the wavefunction and energy in a periodic potential?
4. Give a formula for the density of states of electrons in a periodic potential. What is a van Hove singularity?
7. Chapter 9 - Weak periodic potential
1. What is the Fourier transform of Schrodinger's equation in a periodic potential?
2. Be able to solve this Schrodinger equation near a Bragg plane where one Fourier component dominates.
3. What happens near a Bragg plane to the energy?
4. What are the Brillouin zones and why are they imporant for a weak periodic potential?
8. Chapter 10 - Tight binding method
1. What is the idea behind the tight binding approximation?
2. What is the form of the tight binding wavefunction?
3. Be able to solve some simple tight binding models in one and two dimensions.
9. Chapter 12 - Semiclassical model of electron dynamics
1. What two equations are solved in the semiclassical model of electron dynamics (without scattering)?
2. How much current is carrier in a filled band? Why?
3. Explain how states in almost filled band with E proportional to -k2 may be regarded as holes.
4. Describe the semiclassical motion of electrons in periodic potential in a uniform magnetic field.
10. Chapter 13 - Semiclasscial theory (relaxation time approx.)
1. Write down the Boltzmann equation with in the relaxation time approximation.
2. What is the electrical current, energy current, and heat current in terms of the distribution function.
3. Solve the Boltzmann equation for the electrical conductivity.