DERIVE a 6x6 Hamiltonian for bulk semiconductors

[pd_crew]

URGENT x 10 DERIVE a 6x6 Hamiltonian for bulk semiconductors

Okay here is a little challenge for you guys. Try and test your skill a little. First 10 people to properly derive a 6x6 Hamiltonian for bulk semiconductors will gain bragging rights in this forum.

 

[pd_crew]

would a 6 x 6 be two 3x3s across the diagnol but symmetric?
h11 h12 h13 0 0 0
h21 h22 h23 0 0 0
h31 h32 h33 0 0 0
0 0 0 h11 h12 h13
0 0 0 h21 h22 h23
0 0 0 h31 h32 h33

 

[Dr Transport]

Start with the 3 p-states, and use the $\vec{k} \times \vec{p}$ Hamiltonian to work out the states...You have to include spin and utilize the spin-orbit corrections to get the correct form of the matrix. Worked the $8 \times 8$ version for my dissertation years ago which involved the s-states.