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

JHU Logo
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
Previous Slide Next Slide
Image 0
The Drude model described previously assumed a free electron gas within the crystal lattice. New insight can be obtained by assuming that the electron gas is Nearly Free.

A nearly free electron gas will have energy levels approximating the truly-free electron gas - namely E=(1/2m)p2. The energy is quadratic with respect to the momentum, and hence is quadratic with respect to wavevector k. Note, however, that due to the Bloch translational invariance, there are degeneracies on the Bloch Planes located midway between atoms. Here, the parabolic energy spectrum intersects, and a degenercy exists.

Recall from elementary quantum mechanical degenerate perturbation theory the action of the perturbing Hamiltonian. The perturbation usually has the effect of lifting the degeneracy, for example the fine structure of hydrogen.

The effect of the perturbations caused by the gas NOT being perfectly free essentially lifts the perturbation, and creates a gap at the Bragg plane.