DERIVE a 6x6 Hamiltonian for bulk semiconductors

Click For Summary
SUMMARY

The discussion focuses on deriving a 6x6 Hamiltonian for bulk semiconductors, emphasizing the need to incorporate spin and spin-orbit corrections. Participants are encouraged to utilize the \(\vec{k} \times \vec{p}\) Hamiltonian approach, starting with the three p-states. The structure of the Hamiltonian is proposed as two 3x3 matrices across the diagonal, with specific elements outlined. Previous experience with an 8x8 Hamiltonian is mentioned as a reference point for complexity.

PREREQUISITES
  • Understanding of Hamiltonian mechanics in quantum physics
  • Familiarity with \(\vec{k} \times \vec{p}\) perturbation theory
  • Knowledge of spin and spin-orbit coupling in semiconductors
  • Experience with matrix algebra and symmetry in physics
NEXT STEPS
  • Research the derivation of the \(\vec{k} \times \vec{p}\) Hamiltonian in semiconductor physics
  • Study the role of spin-orbit coupling in semiconductor band structures
  • Explore the construction of 8x8 Hamiltonians for more complex semiconductor systems
  • Examine case studies of Hamiltonian applications in bulk semiconductor research
USEFUL FOR

Physicists, semiconductor researchers, and graduate students specializing in condensed matter physics or quantum mechanics will benefit from this discussion.

pd_crew
Messages
3
Reaction score
0
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.
 
Last edited:
Physics news on Phys.org
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
 
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.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 6 ·
Replies
6
Views
3K
Replies
10
Views
21K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
4K
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 5 ·
Replies
5
Views
4K