Physics 541 A quantum approach to condensed matter physics

Define reciprocal lattice g such that

Polarization directions

Example - heat capacity

Thermal conductivity and thermal expansion depend on phonon interactions

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

But remember that classically So

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

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

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

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