Differences Between Vibrating Atoms and Electrons in a Crystal (5 minutes)

  • Vibrations of atoms in a crystal:
    1. Involves analyzing discrete periodic system with many springs and masses. The movement of the masses is described using envelope functions. (Add image: pplecdifferences1)
    2. Boundary conditions result in normal modes (envelope functions where all atoms move with the same frequency).
    3. Time dependence: $e^{i \omega t}$.
  • Electrons in a crystal:
    1. Involves analyzing a periodic system with one electron and many atoms. The probability of finding one electron somewhere amongst the atoms is described using envelope functions. (Add image:pplecdifferences2)
    2. Boundary conditions result in eigenstates (eigenstates are the analog of normal modes).
    3. Time dependence evolves from the Schrodinger Equation: $e^{i\frac{E}{\hbar}t}$.


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