Transcript reciprocal lattice g

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
So
One spinless electron
So
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
=