Link to pdf version of Slides for Lecture 2

Reading: Text: Chapter 4, which is essentially the same as given in texts on solid state physics.

The background needed for this lecture is basic quantum mechanics at the level of the first graduate course and a course in basic solid state physics.

1. Crystal Periodicity
• Crystal Structure = Lattice + Basis
• Translation symmetry
• Reciprocal Lattice
• Brilluoin Zone
• Types of bonding for various types of crystals
2. Bloch Theorem for excitations in crystals
• Proof by group theory
• Proof by Fourier Expansion
• Applies to any excitations - phonons, electrons, etc.
3. Qualitative discussion of Bloch functions. Zone center, Zone boundary
4. The first qualitative estimates of band widths in solids
• How to predict band widths in a crystal knowing only atomic wavefunctions
• This information (plus a little knowledge of the shell structure of atoms) shows why: 1 covalent materials tend to be wide-band materials with more than one atom per cell, 2) transition metals are likely to be magnetic, expected properties of rare earths, ...
5. Conclusions