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:

- Chapter 1 - Drude theory
- What is the Drude model for metals?
- Calculate the conductivity in the Drude model (see HW problem).

- Chapter 2 - Sommerfeld theory
- How does the Sommerfeld model differ from the Drude model?
- Express the density, Fermi velocity, and Fermi energy in terms of the Fermi wavevector in different dimensions.
- What a typical Fermi energy in eV and k
_{B}T? - What is the density of states? What is the density of states in different dimensions for free electrons?
- Explain the idea behind the Sommerfeld expansion.
- How does the specific heat of metals depend on temperature?

- Chapter 4 - Crystal lattices
- What is a Bravis lattice?
- What are simple cubic, face center cubic, and body center cubic lattices? Give basis vectors for each.
- What is a primitive unit cell? a Wigner-Seitz cell?
- 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?

- Chapter 5 - Reciprocal lattice
- What is the definition of a reciprocal lattice?
- What is the reciprocal lattice of SC, FCC, and BCC lattices?
- Know how to compute a basis for a reciprocal lattice.

- Chapter 6 - X-ray scattering
- Why are X-rays (and not for example visible light) useful for determining crystal structure?
- What are the Bragg and Von Laue formulations of X-ray diffraction?
- Explain the Ewald construction.
- What are the Laue method, the rotating crystal method, and the powder method for X-ray scattering?
- What is the structure factor for a lattice with basis? How does it effect X-ray scattering?

- Chapter 8 - Electrons in a periodic potential
- Give two equivalent statements of Bloch's theorem.
- What is the velocity of an electron in a periodic potential?
- What is the periodicity of the wavefunction and energy in a periodic potential?
- Give a formula for the density of states of electrons in a periodic potential. What is a van Hove singularity?

- Chapter 9 - Weak periodic potential
- What is the Fourier transform of Schrodinger's equation in a periodic potential?
- Be able to solve this Schrodinger equation near a Bragg plane where one Fourier component dominates.
- What happens near a Bragg plane to the energy?
- What are the Brillouin zones and why are they imporant for a weak periodic potential?

- Chapter 10 - Tight binding method
- What is the idea behind the tight binding approximation?
- What is the form of the tight binding wavefunction?
- Be able to solve some simple tight binding models in one and two dimensions.

- Chapter 12 - Semiclassical model of electron dynamics
- What two equations are solved in the semiclassical model of electron dynamics (without scattering)?
- How much current is carrier in a filled band? Why?
- Explain how states in almost filled band with E proportional to -k
^{2}may be regarded as holes. - Describe the semiclassical motion of electrons in periodic potential in a uniform magnetic field.

- Chapter 13 - Semiclasscial theory (relaxation time approx.)
- Write down the Boltzmann equation with in the relaxation time approximation.
- What is the electrical current, energy current, and heat current in terms of the distribution function.
- Solve the Boltzmann equation for the electrical conductivity.