Week 3

Lecture 5, 5 February, 13.15-15.00, FL51

Electrons in periodic potential. Bloch theorem. Crystal momentum.
Nearly free electron approximation.

Reading

A&M: Chapter 8, 9.

Review questions

1. Define and discuss: Bloch wave function, crystal momentum, band structure.
2. Discuss the differences of the Sommerfeld and Bloch descriptions of the electron states in a crystal. In particular, focus on quantum numbers, the range of quantum numbers, the energy, the velocity, and the structure of the wave functions.
3. Derive Bloch's theorem.
4. How many Bloch states are there in 1BZ? 5. Explain the reduced and the extended zone scheme.
6. What is the basic assumption behind the "nearly-free-electron approximation"?
7. Which electron states are most influenced by a weak periodic potential?
8. Sketch the energy bands in a one-dimensional metal in the extended, reduced, and repeated zone scheme for free electrons and according to the nearly free electron approximation.
9. Define the Brillouin zones in terms of Bragg planes.

Home task

1. A&M, problems 5.1; 5.2a.
2. Find volume of primitive cell of reciprocal lattice.

Lecture 6, 7 February, 10.00-12.00, FL51

Electrons in periodic potential. Nearly free electron approximation.