Transcript V(r)

Physics 541
A quantum approach to condensed
matter physics
One-electron approximation
Born-Oppenheimer approximation
Core electrons tightly bound, so just consider conduction electrons
For free electrons (V = 0)
When V = V(r), we get Bloch’s theorem
What is a “hole”?
Put
At top of band
Negative effective mass!
At bottom of band
Write
2-plane-wave model works well for energies
Conduction electron states must be orthogonal to the core states,
so they really have a lot of wiggles
Orthogonalized plane waves
Define projection operator
Put
where
This is the pseudopotential operator
will not do much when acting on
the smooth wavefunction
Fibonacci chain