Quick and Dirty Preview of Solid State Physics
JHU Seal Quick and Dirty Preview of Solid State Physics

Jeffrey Wasserman
Second Year Seminar
Presented April 9, 2002
Johns Hopkins University

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Table of Contents

  1. Presentation Title
  2. What is Solid State Physics?
  3. What does Solid State Physics entail?
  4. Relative Importance of Solid State Physics
  5. Why is there interest in Solid State Physics?
  6. Historical Approach Part I - The Drude Model
  7. Successes of the Drude Model
  8. Historical Approach Part II - The Sommerfeld Model
  9. Inadequacies of the Drude and Sommerfeld Models
  10. Crystals and Lattices
  11. More About Lattices
  12. Reciprocal Lattice
  13. X-Ray Diffraction and Scattering from Lattices
  14. Effects of the Periodicity of the Lattice
  15. Bloch Waves and Brillouin Zones
  16. Brillouin Zones in Three Dimensions
  17. The Fermi Energy and the Fermi Surface
  18. The Nearly-Free Electron Gas
  19. Illustration of Nearly-Free Electron Gas in 1 Dimension
  20. Nearly-Free Electron Gas and Conductivity
  21. Nearly-Free Electron Gas in Aluminum
  22. Tightly-Bound Electrons - Overview
  23. Tightly-Bound Electrons and Band Structure
  24. Further Topics and Applications
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At first glance, one might think that all Bravais lattices are really just the same thing. That is, all have a unit cell of a parallelpiped. The difference comes in when dealing with the three lattice vectors a, b, and c.

Different point group symmetries are what denote the different lattices. These include varying degrees of rotational symmetry and parity. For example, a simple cubic lattice can rotate around either the x, y, or z axis by 90° without change. If one now extended only one of the lattice vectors, say doubling the length of a, one can only get the rotational invariance about 2 axes, not three. Differences such as these define the lattices groups.

These differences also have profound effect on the lattice properties, as they determine how the Hamiltonians behave under varying symmetry groups when the lattice is looked at quantum mechanically.