1. Physics 541 A quantum approach to condensed matter physics

2. Define reciprocal lattice g such that

3. Polarization directions

5. Example - heat capacity

7. Thermal conductivity and thermal expansion depend on phonon interactions

8. We need a better definition for quantum mechanical magnetic moment In classical mechanics the Lorentz force is Lagrange’s equation states that This requires

9. But remember that classically So

11. One spinless electron Add magnetic field This is like a perturbation added to

12. Spin is a relativistic effect. Expand Dirac equation in powers of 1/c Spin s is like orbital angular momentum L

14. Heisenberg model Saturation -- all spins in z direction Magnetization Near saturation all will be small

16. Bohr magneton At low temperatures only small excited, for which =